Displacement devices and methods for fabrication, use and control of same

ABSTRACT

Displacement devices comprise a stator and a moveable stage. The stator comprises a plurality of coils shaped to provide pluralities of generally linearly elongated coil traces in one or more layers. Layers of coils may overlap in the Z-direction. The moveable stage comprises a plurality of magnet arrays. Each magnet array may comprise a plurality of magnetization segments generally linearly elongated in a corresponding direction. Each magnetization segment has a magnetization direction generally orthogonal to the direction in which it is elongated and at least two of the magnetization directions are different from one another. One or more amplifiers may be connected to selectively drive current in the coil traces and to thereby effect relative movement between the stator and the moveable stage.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/595,941 filed 15 May 2017, which is, in turn, a continuation of U.S.patent application Ser. No. 14/920,885 filed 23 Oct. 2015, which is, inturn, a continuation of U.S. patent application Ser. No. 14/354,515having a 35 USC 371 date of 25 Apr. 2014, which is, in turn, a nationalphase entry of PCT application No. PCT/CA2012/050751 having aninternational filing date of 22 Oct. 2012. PCT application No.PCT/CA2012/050751 claims the benefit of the priority of U.S. applicationNo. 61/551,953 filed 27 Oct. 2011 and of U.S. application No. 61/694,776filed 30 Aug. 2012. All of the prior applications in referred to in thisparagraph are hereby incorporated herein by reference.

TECHNICAL FIELD

The invention relates to displacement devices. Particular non-limitingembodiments provide displacement devices for use in the semiconductorfabrication industry.

BACKGROUND

Motion stages (XY tables and rotary tables) are widely used in variousmanufacturing, inspection and assembling processes. A common solutioncurrently in use achieves XY motion by stacking two linear stages (i.e.a X-stage and a Y-stage) together via connecting bearings.

A more desirable solution involves having a single moving stage capableof XY motion, eliminating additional bearings. It might also bedesirable for such a moving stage to be able to provide at least some Zmotion. Attempts have been made to design such displacement devicesusing the interaction between current-carrying coils and permanentmagnets. Examples of efforts in this regard include the following: U.S.Pat. Nos. 6,003,230; 6,097,114; 6,208,045; 6,441,514; 6,847,134;6,987,335; 7,436,135; 7,948,122; US patent publication No. 2008/0203828;W. J. Kim and D. L. Trumper, High-precision magnetic levitation stagefor photolithography. Precision Eng. 22 2 (1998), pp. 66-77; D. L.Trumper, et al, “Magnet arrays for synchronous machines”, IEEE IndustryApplications Society Annual Meeting, vol. 1, pp. 9-18, 1993; and J. W.Jansen, C. M. M. van Lierop, E. A. Lomonova, A. J. A. Vandenput,“Magnetically Levitated Planar Actuator with Moving Magnets”, IEEE Tran.Ind. App., Vol 44, No 4, 2008.

There is a general desire to provide displacement devices havingcharacteristics that improve upon those known in the prior art.

The foregoing examples of the related art and limitations relatedthereto are intended to be illustrative and not exclusive. Otherlimitations of the related art will become apparent to those of skill inthe art upon a reading of the specification and a study of the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments are illustrated in referenced figures of thedrawings. It is intended that the embodiments and figures disclosedherein are to be considered illustrative rather than restrictive.

FIG. 1A is a partial schematic isometric view of a displacement deviceaccording to a particular embodiment of the invention.

FIG. 1B is a partial schematic cross-sectional view of the FIG. 1Adisplacement device along the line 1B-1B.

FIG. 1C is a partial schematic cross-sectional view of the FIG. 1Adisplacement device along the line 1C-1C.

FIG. 1D shows additional detail of one of the Y-magnet arrays of theFIG. 1A displacement device in accordance with a particular embodiment.

FIG. 1E shows additional detail of one of the X-magnet arrays of theFIG. 1A displacement device in accordance with a particular embodiment.

FIG. 2 is a schematic partial cross-sectional view of a single layer ofcoil traces which may be used in the FIG. 1 displacement devices andwhich are useful for showing a number of coil parameters.

FIGS. 3A-3F are schematic partial cross-sectional views of single layersof coil traces having different layouts which may be used in the FIG. 1displacement device.

FIGS. 4A and 4B are schematic partial cross-sectional views of multiplelayers of coil traces having different layouts which may be used in theFIG. 1 displacement device.

FIG. 5 is a schematic partial view of a single layer of coil tracesshowing a group connection scheme which may be used in the FIG. 1displacement device.

FIGS. 6A and 6B are schematic partial cross-sectional views of layoutsof magnet arrays which may be used in the FIG. 1 displacement device andwhich are useful for showing a number of magnet array parameters.

FIGS. 7A-7L show additional details of magnet arrays suitable for usewith the FIG. 1 displacement device in accordance with particularembodiments.

FIGS. 8A-8L show additional details of magnet arrays suitable for usewith the FIG. 1 displacement device in accordance with particularembodiments.

FIGS. 9A and 9B are schematic cross-sectional views of pairs of paralleladjacent magnet arrays according to particular embodiments suitable foruse with the FIG. 1 displacement device and showing the magnetizationdirections of their corresponding magnetization segments.

FIGS. 10A-10D are schematic cross-sectional views of layouts of magnetarrays which may be used in the FIG. 1 displacement device in accordancewith other embodiments.

FIGS. 11A-11C are schematic cross-sectional views of magnet arrays andcoil traces used to demonstrate a theoretical field folding principle.

FIG. 11D is a schematic cross-sectional view showing one layer of coiltraces and a single magnet array that may be used in the FIG. 1displacement device and how the field folding principle of FIGS. 11A-11Cmay be used in practice.

FIG. 12 is a schematic cross-sectional view showing one layer of coiltraces and a single magnet array which are useful for describing thedetermination of current commutation.

FIGS. 13A and 13B schematically depict an assumed magnet arrayconfiguration which can be used to determine suitable currents formagnet arrays having non-magnetic spacers.

FIG. 14A schematically illustrates one embodiment of a sensing systemsuitable for use with the FIG. 1 displacement device for separatelymeasuring the positions of the moveable stage and stator relative to ametrology frame. FIGS. 14B and 14C schematically illustrate otherembodiments of sensor systems suitable for use with the FIG. 1displacement device.

FIG. 15 shows a schematic block diagram of a control system suitable foruse in controlling the FIG. 1 displacement device.

FIGS. 16A-16D schematically depict a technique for interchangingmoveable stages between multiple stators according to one embodiment ofthe invention.

FIG. 17A schematically depicts a technique for interchanging moveablestages between multiple stators according to another embodiment of theinvention. FIG. 17B schematically depicts how two moveable stages can becontrolled with six degrees of freedom on one stator.

FIG. 18 schematically illustrates an apparatus for moving a plurality ofmoveable stages through a plurality of different stages.

FIG. 19A is a horizontal cross-sectional view of a rotary displacementdevice according to an embodiment of the invention. FIGS. 19B and 19Crespectively depict a bottom cross-sectional view of the moveable stage(rotor) of the FIG. 19A displacement device and a top view of the statorof the FIG. 19A displacement device.

FIG. 19D is a bottom cross-sectional view of a moveable stage (rotor)according to another embodiment which may be used with the FIG. 19Adisplacement device.

FIG. 19E is a top view of a stator according to another embodiment whichmay be used with the FIG. 19A displacement device.

FIGS. 20A-20C schematically depict displacement devices according toother embodiments having different relative orientations of coil tracesand magnet arrays.

FIGS. 21A-21C schematically depict cross-sectional views of magnetarrays having different numbers of magnetization directions within aparticular magnetic spatial period.

FIG. 22A shows a coil trace layout according to another embodiment whichmay be used in the FIG. 1 displacement device. FIG. 22B illustrates apair of adjacent layers of Y-oriented coil traces which may be used inthe FIG. 1 displacement device.

FIGS. 23A-23F show a number of Y-oriented coil traces which (whilegenerally linearly elongated in the Y-direction) exhibit periodicspatial variation which extends in the X-direction over their respectiveY-dimensions and which may be used in the FIG. 1 displacement device.

FIGS. 24A and 24B show a pair of Y-oriented coil traces which haveperiodic variation which may be superposed to provide the Y-orientedcoil trace of FIG. 24C.

FIGS. 25A-25D show various embodiments of magnet arrays having offset orshifted sub-arrays which may be used in the FIG. 1 displacement device.

FIGS. 26A, 26B and 26C show a number of Y-magnet arrays which exhibitperiodic spatial variation which extends in the X-direction over theirrespective Y-dimensions and which may be used in the FIG. 1 displacementdevice.

FIGS. 27A and 27B respectively depict a top view of a number of coiltraces and a cross-sectional view of a coil trace which comprisemultiple sub-traces in accordance with a particular embodiment which maybe used in the FIG. 1 displacement device.

FIGS. 28A and 28B show various views of circular cross-section coiltraces according to another embodiment which may be used with the FIG. 1displacement device. FIGS. 28C and 28D show embodiments of how coiltraces may comprise multiple sub-traces having circular cross-section.

DESCRIPTION

Throughout the following description specific details are set forth inorder to provide a more thorough understanding to persons skilled in theart. However, well known elements may not have been shown or describedin detail to avoid unnecessarily obscuring the disclosure. Accordingly,the description and drawings are to be regarded in an illustrative,rather than a restrictive, sense.

Displacement devices are provided which comprise a stator and a moveablestage. The stator comprises a plurality of coils shaped to providepluralities of generally linearly elongated coil traces in one or morelayers. Layers of coils may overlap in the Z-direction. The moveablestage comprises a plurality of magnet arrays. Each magnet array maycomprise a plurality of magnetization segments generally linearlyelongated in a corresponding direction. Each magnetization segment has amagnetization direction generally orthogonal to the direction in whichit is elongated and at least two of the of the magnetization directionsare different from one another. One or more amplifiers may beselectively connected to drive current in the coil traces and to therebyeffect relative movement between the stator and the moveable stage.

Particular Embodiment

FIG. 1A is a partial schematic isometric view of a displacement device100 according to a particular embodiment of the invention. FIGS. 1B and1C are partial schematic cross-sectional views of displacement device100 along the lines 1B-1B and 1C-1C respectively. Displacement device100 comprises a moveable stage 110 and a stator stage 120. Moveablestage 110 comprises a plurality (e.g. 4 in the illustrated embodiment)of arrays of permanent magnets 112A, 112B, 112C, 112D (collectively,magnet arrays 112). Stator stage 120 comprises a plurality of coils 122.As explained in more detail below, each of coils 122 is elongated alonga particular dimension, such that in a working region 124 of stator 120(i.e. a region of stator 120 over which moving stage 110 can move),coils 122 effectively provide linearly elongated coil traces 126. Asexplained in more detail below, each of coil traces 126 comprises acorresponding axis along which it is linearly elongated. For clarity,only a portion of the working area 124 of stator 120 is shown in theviews of FIGS. 1A-1C. It will be appreciated that outside of the partialviews of FIGS. 1A-1C, coils 122 have loops which are not linearlyelongated. The loops of coils 122 are located sufficiently far outsideof the working area 124 of stator 120 that these loops do not have animpact on the operation of device 100.

In the illustrated embodiment (as best seen in FIG. 1C), stator 120comprises a plurality (e.g. 4 in the illustrated embodiment) of layers128A, 128B, 128C, 128D (collectively, layers 128) of coil traces 126,with each pair of coil trace layers 128 separated from one another by anelectrically insulating layer 130. It will be appreciated that thenumber of layers 128 in stator 120 may be varied for particularimplementations and that the number of layers 128 shown in theillustrated embodiment is convenient for the purposes of explanation. Inthe illustrated embodiment, each layer 128 comprises coil traces 126that are linearly elongated along axes that are parallel to one another.In the case of the illustrated embodiment, layers 128A, 128C comprisecoil traces 126Y which are generally linearly elongated in directionsparallel to the Y-axis and layers 128B, 128D comprise coil traces 126Xwhich are generally linearly oriented in directions parallel to theX-axis. Coil traces 126Y which are generally linearly oriented along theY-axis may be referred to herein as “Y-coils” or “Y-traces” and, asexplained in more detail below, may be used to move moveable stage 110in the X and Z directions. Similarly, coil traces 126X which aregenerally linearly oriented along the X-axis may be referred to hereinas “X-coils” or “X-traces” and, as explained in more detail below, maybe used to move moveable stage 110 in the Y and Z directions.

In the illustrated embodiment (as shown best in FIG. 1B), moveable stage110 comprises four magnet arrays 112. In some embodiments, moveablestage 110 may comprise more than four magnet arrays 112. Each magnetarray 112A, 112B, 112C, 112D comprises a plurality of correspondingmagnetization segments 114A, 114B, 114C, 114D (collectively,magnetization segments 114) having different magnetization directions.In the illustrated embodiment, each magnetization segment 114 isgenerally elongated along a corresponding axial dimension. The elongatedshape of magnetization segments 114 of the illustrated embodiment isshown best in FIG. 1B. It can be seen that in the case of theillustrated embodiment, magnetization segments 114A of magnet array 112Aand magnetization segments 114C of magnet array 112C are generallyelongated in directions parallel to the X-axis and magnetizationsegments 114B of magnet array 112B and magnetization segments 114D ofmagnet array 112D are generally elongated in directions parallel to theY-axis. Because of the direction of elongation of their respectivemagnetization segments 114: magnet arrays 112A, 112C may be referred toherein as “X-magnet arrays” 112A, 112C and their correspondingmagnetization segments 114A, 114C may be referred to herein as“X-magnetization segments”; and magnet arrays 112B, 112D may be referredto herein as “Y-magnet arrays” 112B, 112D and their correspondingmagnetization segments 114B, 114D may be referred to herein as“Y-magnetization segments”.

FIG. 1C schematically shows the orientation of the magnetization of thevarious magnetization segments 114B of Y-magnet array 112B in accordancewith a particular non-limiting example. More particularly, theschematically illustrated arrows in Y-magnet array 112B of FIG. 1C showthe magnetization directions of the various magnetization segments 114B.Also, within each magnetization segment 114B, the shaded regionsrepresent the north poles of the magnets and the white regions representthe south poles of the magnets.

FIG. 1D shows a cross-sectional view of Y-magnet array 112B in moredetail. It can be seen that Y-magnet array 112B is divided into a numberof magnetization segments 114B along the X-axis and that themagnetization directions of the various segments 114B are oriented indirections orthogonal to the Y-axis—i.e. the magnetization directions ofthe magnetization segments 114B are orthogonal to the Y-axis directionalong which magnetization segments 114B are elongated. It may also beobserved from FIG. 1D that the magnetization directions of magnetizationsegments 114B have a spatial periodicity with a period (or wavelength) λalong the X-axis. This spatial periodicity λ of the magnetizationdirections of the magnetization segments 114 of a magnet array 112 maybe referred to herein as the magnetic period λ, magnetic spatial periodλ, magnetic wavelength λ or magnetic spatial wavelength λ.

In the illustrated FIG. 1D embodiment, Y-magnet array 112B has a totalX-axis width of 2λ—i.e. two periods of the magnetic period λ. This isnot necessary. In some embodiments, Y-magnet array 112B has a totalX-axis width W_(m) given by W_(m)=N_(m)λ where N_(m) is a positiveinteger.

In the case of the illustrated FIG. 1D embodiment, magnetizationsegments 114B comprise four different magnetization directions: +Z, −Z,+X, −X which together provide a magnetic spatial period λ. This is notnecessary. In some embodiments, magnetization segments 114B may compriseas few as two magnetization directions to provide a magnetic spatialperiod λ and in some embodiments, magnetization segments 114B maycomprise more than four magnetization directions to provide a magneticspatial period λ. The number of different magnetization directions of amagnet array 112 that make up a complete spatial magnetic period λ maybe referred to herein as N_(t). Regardless of the number N_(t) ofmagnetization directions of magnetization segments 114B, themagnetization direction of each segment 114B is oriented generallyorthogonally to the Y-axis. FIG. 1D also shows that, in the illustratedembodiment, the X-axis width of a magnetization segment 114B is either:λ/(2Nt) or λ/N_(t). In the case of the FIG. 1D embodiment, where thenumber N_(t) of magnetization directions is N_(t)=4, the X-axis width ofmagnetization sections 114B is either λ/8 (as is the case for the edgesegments labeled A, I) or λ/4 (as is the case for the interior segmentslabeled B,C,D,E,F,G,H).

Another observation that may be made in the case of the illustrated FIG.1D embodiment is that the magnetization of magnetization segments 114Bis mirror symmetric about a central Y-Z plane 118 (i.e. a plane 118 thatextends in the Y-axis and Z-axis directions and that intersects magnetarray 112B at the center of its X-axis dimension). While not explicitlyshown in FIG. 1D, in some embodiments magnet array 112B may be providedwith a non-magnetic spacer at the center of its X-axis dimension. Moreparticularly, magnetization segment 114B at the center of the X-axisdimension of magnet array 112B (i.e. the segment labeled E in theillustrated embodiment) may be divided into two segments of widthλ/(2Nt)=λ/8 and a non-magnetic spacer may be inserted therebetween. Asexplained in more detail below, such a non-magnetic spacer can be usedto cancel disturbance forces/torques generated by higher order magneticfields. Even with such non-magnetic spacer, magnet array 112B and itsmagnetization segments 114B will still exhibit the properties that: thatthe magnetization directions of the various segments 114B are orientedin directions orthogonal to the Y-axis; the X-axis widths of the varioussegments 114B will be either: λ/(2Nt) (for the outer segments A,I andthe two segments formed by dividing segment E) or λ/Nt (for the interiorsegments B,C,D,F,G,H); and the magnetization of magnetization segments114B is mirror symmetric about central Y-Z plane 118.

Other than for its location on moveable stage 110, the characteristicsof Y-magnet array 112D and its magnetization segments 114D may besimilar to those of Y-magnet array 112B and its magnetization segments114B.

FIG. 1E shows a cross-sectional view of X-magnet array 112A in moredetail. It will be appreciated that X-magnet array 112A is divided,along the Y-axis, into a number of magnetization segments 114A which aregenerally linearly elongated in the X-axis direction. In the illustratedembodiment, the characteristics of X-magnet array 112A and itsmagnetization segments 114A may be similar to those of Y-magnet array112B and its magnetization segments 114B, except that the X and Ydirections are swapped. For example, the magnetization directions ofmagnetization segments 114A have a spatial periodicity with a period (orwavelength) λ along the Y-axis; the width W_(m) of X-magnet array 112Ain the Y-direction is given by W_(m)=N_(m)λ where N_(m) is a positiveinteger; the magnetization directions of the various magnetizationsegments 114A are oriented in directions orthogonal to the X-axis; theY-axis widths of the various magnetization segments 114A are either:λ/(2N_(t)) (for the outer segments A,I) or λ/N_(t) (for the interiorsegments B,C,D,E,F,G,H), where N_(t) represents the number of differentmagnetization directions in magnet array 112A; and the magnetization ofmagnetization segments 114A is mirror symmetric about central X-Z plane118.

Other than for its location on moveable stage 110, the characteristicsof X-magnet array 112C and its magnetization segments 114C may besimilar to those of X-magnet array 112A and its magnetization segments114A.

Referring to FIGS. 1B and 1C, the operation of displacement device 100is now explained. FIG. 1C shows how moveable stage 110 is spacedupwardly apart from stator 120 in the Z-direction. This space betweenstator 120 and moveable stage 110 can be maintained (at least in part)by Z-direction forces created by the interaction of coils 122 on stator120 with magnet arrays 112 on moveable stage 110 as discussed below. Insome embodiments, this space between stator 120 and moveable stage 110can be maintained using additional lifting and/or hoisting magnets,aerostatic bearings, roller bearings and/or the like (not shown), as isknown in the art.

FIG. 1B shows four sets of active coil traces 132A, 132B, 132C, 132D(collectively, coil traces 132), each of which (when carrying current)is primarily responsible for interacting with a corresponding one ofmagnet arrays 112A, 112B, 112C, 112D to impart forces which causemoveable stage 110 to move. More particularly: when coil traces 132A arecarrying current, they interact with X-magnet array 112A to impartforces on moveable stage 110 in the Y and Z directions; when coil traces132B are carrying current, they interact with Y-magnet array 112B toimpart forces on moveable stage 110 in the X and Z directions; when coiltraces 132C are carrying current, they interact with X-magnet array 112Cto impart forces on moveable stage 110 in the Y and Z directions; andwhen coil traces 132D are carrying current, they interact with Y-magnetarray 112D to impart forces on moveable stage 110 in the X and Zdirections.

It will be appreciated that coil traces 132 shown in FIG. 1B can beselectively activated to impart desired forces on moveable stage 110 andto thereby control the movement of moveable stage 110 with six degreesof freedom relating to the rigid body motion of moveable stage 110. Asexplained further below, coil traces 132 can also be controllablyactivated to control some flexible mode vibrating motion of moveablestage 110. When moveable stage 110 is shown in the particular positionshown in FIG. 1B, coil traces other than coil traces 132 may beinactive. However, it will be appreciated that as moveable stage 110moves relative to stator 120, different groups of coil traces will beselected to be active and to impart desired forces on moveable stage110.

It may be observed that the active coil traces 132 shown in FIG. 1Bappear to interact with other magnet arrays. For example, when carryingcurrent, coil traces 132C interact with X-magnet array 112C as discussedabove, but coil traces 132C also pass under a portion of Y-magnet array112B. One might expect that, the current in coil traces 132C mightinteract with the magnets in Y-magnet array 112B and impart additionalforces on moveable stage 110. However, because of the aforementionedcharacteristics of Y-magnet array 112B, the forces that might have beencaused by the interaction of coil traces 132C and the magnetizationsegments 114B of Y-magnet array 112B cancel one another out, such thatthese parasitic coupling forces are eliminated or kept to a minimallevel. More particularly, the characteristics of Y-magnet array 112Bthat eliminate or reduce these cross-coupling forces include: Y-magnetarray 112B includes magnetization segments which are generally elongatedin the Y-direction with varying magnetizations which are orientedorthogonally to the Y-direction; the X-dimension width Wm of Y-magnetarray 112B is Wm=Nmλ where Nm is an integer and λ is the magnetic periodλ described above; and Y-magnet array 112B is mirror symmetric about aY-Z plane that runs through the center of the X-dimension of Y-magnetarray 112B.

For example, the X-dimension width Wm of Y-magnet array 112B being aninteger number of magnetic wavelengths (Wm=Nmλ) minimizes force couplingwith non-aligned coil traces 132C, because the net force on magnet array112B will integrate to zero (i.e. will cancel itself out) over eachwavelength λ of magnet array 112B. Also, the mirror-symmetry of Y-magnetarray 112B about a Y-Z plane that is orthogonal to the X-axis and runsthrough the center of the X-dimension of Y-magnet array 112B minimizesthe net moment (about the Z-axis and about the Y-axis) due to theinteraction of magnet array 112B with X-oriented coil traces 132C.Similar characteristics of Y-magnet array 112D eliminate or minimizecross-coupling from coil traces 132A.

In an analogous manner, the characteristics of X-magnet array 112Aeliminate or reduce cross-coupling forces from coil traces 132B. Suchcharacteristics of X-magnet array 112A include: X-magnet array 112Aincludes magnetization segments which are generally elongated in theX-direction with varying magnetizations which are oriented orthogonallyto the X-direction; the Y-dimension width Wm of X-magnet array 112A isWm=Nmλ where Nm is an integer and λ is the magnetic period λ describedabove; and X-magnet array 112A is mirror symmetric about a X-Z planethat is orthogonal to the y-axis and runs though the center of theY-dimension of X-magnet array 112A. Similar characteristics of X-magnetarray 112C eliminate or minimize cross coupling from coil traces 132D.

Coil Array

Additional detail of stator 120 and its coil arrays is now provided. Asdescribed above, stator 120 comprises a plurality of layers 128 of coiltraces 126 which are generally linearly oriented in the working region124. Each layer 128 comprises coil traces 126 that are generally alignedwith one another (e.g. generally linearly elongated in the samedirection). In the illustrated embodiment of FIGS. 1A-1E, verticallyadjacent layers 128 (i.e. layers 128 next to one another in theZ-direction) comprise coil traces 126 that are orthogonally orientedwith respect to one another. For example, coil traces 126Y in layers128A, 128C (FIG. 1C) are generally linearly oriented parallel to theY-axis and coil traces 126X in layers 128B, 128D are generally linearlyoriented parallel to the X-axis. It will be appreciated that the numberof layers 128 of coil traces 126 in stator 120 need not be limited tothe four traces shown in the illustrated embodiment. In general, stator120 may comprise any suitable number of layers 128 of coil traces 126.Further, it is not a requirement that the orientations of coil traces126 in vertically adjacent layers 128 be different from one another.Some embodiments may comprise a number of vertically adjacent layers 128of Y-oriented traces 126Y followed by a number of vertically adjacentlayers 128 of X-oriented coil traces 126X.

Stator 120 and its arrays of coils 122 may be fabricated using one ormore printed-circuit boards (PCBs). PCBs can be manufactured usingstandard PCB fabrication, flat-panel display lithography, lithographyand/or similar technology known in the art to provide coils 122 and coiltraces 126. Insulator layers 130 (such as FR4 core, prepreg, ceramicmaterial and/or the like) may be fabricated or otherwise insertedbetween coil layers 128. One or more coil layers 128 may be stackedtogether (i.e. in the Z-direction) in a single PCB board. In someembodiments, coil traces 126 generally elongated in the same direction(at different layers 128) may be connected in parallel or serially,depending on via design and/or connecting methods for the ends of coiltraces 126. In some embodiments, coil traces 126 generally elongated inthe same direction (at different layers 128) are not connected to oneanother.

Coils 122 fabricated using PCB technology can accommodate sufficientcurrent for controlling the motion of moveable stage 110. By way ofnon-limiting example, each coil 122 can be made from 6 oz copper (about200-220 μm thick) or more. As discussed above, in active region 124,each coil 122 is in the shape of a flat strip or coil trace 126, whichprovides good thermal conductivity due to the high ratio of surface areato volume. The inventors have confirmed (via testing) that laminatedcopper can carry a sustained current density of 10 A/mm² with a 50° C.temperature rise above ambient without using an active heat sink.Another advantage of planar layers 128 of coils 122 and coil traces 126is that the naturally stratified conductors that provide coils 122 makethem ideally suitable for carrying AC current, because theself-generated alternating magnetic field can easily penetrate theconductor through top and bottom surfaces but generates only lowself-induced eddy currents.

Multiple PCBs may be aligned side by side in both X and Y directions(similar to floor tiles) to provide the desired X-Y dimensions foractive region 124. Board-to-board lateral connections (in the X and/or Ydirections) may be made at the edges by connecting pads, through-holesof edge-adjacent boards, copper wires and/or using other suitablebridging components of the like for electrically connecting conductorson adjacent PCB boards. In some embodiments, such bridging componentsmay be located underneath the PCB boards (e.g. on the side oppositemoveable stage 110); in some embodiments, such bridging components maybe additionally or alternatively located above the PCB boards or on theside(s) of the PCB boards. When PCBs are connected adjacent to oneanother in the X and/or Y directions, the end terminals (not shown) ofcoils 122 may be located at or near the perimeter of stator 120 for easeof wiring to the drive electronics. Connecting PCBs to one another inthis manner allows displacement device 100 to be easily extended in bothX and Y dimensions for various applications. When PCBs are connected toone another in the X and/or Y dimensions, the total number of coils 122increases linearly with the X-Y dimensions of active area 124 of stator120 (instead of quadratically, as is the case in some prior arttechniques involving so-called “racetrack” coil designs). In someembodiments, coil traces 126 on X-Y adjacent PCB boards may be seriallyconnected to one another to reduce the number of amplifiers (not shown)for driving current through coil traces 126. In some embodiments, coiltraces 126 on X-Y adjacent PCB boards may be individually controlled byseparate amplifiers to increase the flexibility for multi-stageactuation and to reduce heat generation.

A single PCB board may be fabricated to have a thickness (in theZ-direction) of up to 5 mm (or more) using available PCB technology.When thicker boards are required for heavy-duty applications, multiplePCBs can be stacked vertically in the Z direction. Another benefit ofusing PCB technology to fabricate stator 120 is the possibility ofdeploying large numbers of low-profile sensors (such as Hall-effectposition sensor, capacitive position sensors and/or the like) directlyon the board using daisy chain connections.

FIG. 2 is a schematic partial cross-sectional view of a single layer 128of stator 120 and its coil traces 126 which may be used in the FIG. 1displacement device 100. FIG. 2 shows a number of parameters which areused in the description that follows. More particularly, W_(C) is thewidth of single coil trace 126. P_(C) is the coil trace pitch—i.e. thedistance between two adjacent coil traces 126 of the same layer 128.

In some embodiments, each layer 128 of coil traces 126 is fabricatedsuch that: the coil trace pitch P_(C)=λ/N, where N is a positive integerand λ is the above-discussed spatial magnetic wavelength of magnetarrays 112; and W_(C) is set close to P_(C) such that there is a minimumacceptable gap (P_(C)−W_(C)) between adjacent coil traces 126. Forexample, the trace gap P_(C)−W_(C) can be set at 50˜100 μm (e.g. lessthan 200 μm). It will be appreciated that the minimum possibleacceptable trace gap will depend on a number of factors, including,without limitation, the amount of current expected to be carried in eachcoil trace, the capability of the PCB fabrication process and the heatdissipating characteristics of the system 100. FIGS. 3A-3C schematicallydepict a number of possible embodiments of coil trace layers 128 whichare fabricated to have these characteristics. In each of the FIG. 3A-3Cembodiments, P_(C)=λ/6 (i.e. N=6) and W_(C) is set very close to P_(C)such that there is a minimum acceptable gap (e.g. less than 200 μm)between adjacent coil traces 126.

In some embodiments, each layer 128 of coil traces 126 is fabricatedsuch that every MN/2 (where M is another positive integer number)adjacent coil traces 126 form one coil group 134, where coil traces 126in the same group 134 can be either driven by separate amplifiers or beconnected in a star pattern and driven by a multi-phase amplifier. FIGS.3A-3C show a number of different grouping arrangements that exhibitthese characteristics. In FIG. 3A, M=2 and N=6, so each group 134includes 6 adjacent coil traces 126. In some embodiments, each FIG. 3Agroup 134 may be driven by a corresponding three-phase amplifier (notshown). For example, the coil traces 126 labeled A1,B1,C1,A1′,B1′,C1′belong to one group 134. The symbol ′ used in FIG. 3A indicatesreversing current. For example, the electrical current in trace A1′ isthe same as that of trace A1 but in opposite direction. In FIG. 3B, M=1and N=6, so each group 134 includes 3 adjacent coil traces 126. In someembodiments, each FIG. 3B group 134 may be driven by a correspondingthree-phase amplifier (not shown). In FIG. 3C, M=3 and N=6, so eachgroup 134 includes 9 adjacent coil traces 126. In some embodiments, eachFIG. 3C group 134 may be driven by a corresponding three-phase amplifier(not shown). Like FIG. 3A, the symbol ′ used in FIG. 3C indicatesreversing current. It will be appreciated in light of the foregoing thatin general, every 3n (n is a positive integer) adjacent coil traces 126can form one group 134 driven by a corresponding three-phase amplifier.

In some embodiments, each layer 128 of coil traces 126 is fabricatedsuch that the coil-trace width W_(C)=λ/5 and the coil trace pitchP_(C)=λ/k, where k is any number less than 5 and λ is the spatialmagnetic period of magnet arrays 112. Setting W_(C)=λ/5 has theadvantage that such a coil trace width minimizes the effect of fifthorder magnetic fields generated by magnet arrays 112, because of aspatial filtering/averaging effect. FIGS. 3D-3E schematically depict anumber of possible embodiments of coil trace layers 128 which arefabricated to have these characteristics. In each of the FIG. 3D-3Eembodiments, W_(C)=λ/5 and the coil trace pitch P_(C)=λ/k.

In FIG. 3D, W_(C)=λ/5 and

$P_{C} = {\frac{\lambda}{k} = {\frac{\lambda}{3}.}}$It can be seen from FIG. 3D, that adjacent coil traces 126 arerelatively widely spaced apart from one another compared to those of theembodiments shown in FIGS. 3A-3C. In the FIG. 3D embodiment, every 3adjacent coil traces 126 are grouped together to provide groups 134,wherein each group 134 may be driven by a corresponding three-phaseamplifier (not shown). In general, coil traces 126 may be grouped suchthat every 3n (n is a positive integer) adjacent coil traces 126 canform one group 134 which may be driven by one corresponding three-phaseamplifier. FIG. 3E shows a layout where W_(C)=λ/5 and

$P_{C} = {\frac{\lambda}{k} = {\frac{\lambda}{4}.}}$In the FIG. 3E embodiment, every 4 adjacent coil traces 126 are groupedtogether to provide groups 134. Groups 134 of the FIG. 3E embodiment maybe driven by a corresponding two-phase amplifier. As before, the symbol′ used to label coil traces 126 indicates reversing current. In general,coil traces 126 may be grouped such that every 2n (n is a positiveinteger) adjacent coil traces 126 can form one group 134.

FIG. 3F shows a layout which combines the characteristics of the layoutsof FIGS. 3A-3C and of FIGS. 3D-3E. More particularly, in FIG. 3F, thecoil trace pitch P_(C)=λ/5 and W_(C) is set close to P_(C) such thatthere is a minimum acceptable gap between adjacent coil traces. It willbe appreciated that these characteristics are similar to those of theembodiments of FIGS. 3A-3C. However, with W_(C) is set close to P_(C),W_(C) will be almost equal to W_(C)=λ/5 which is the characteristic ofthe embodiment of FIGS. 3D-3E. Accordingly, the layout in FIG. 3F can beused to minimize the effect of fifth order magnetic fields generated bymagnet arrays 112 (as discussed above). In the FIG. 3F embodiment, every5 adjacent coil traces 126 are grouped together to provide groups 134.Groups 134 of the FIG. 3F embodiment may be driven by a correspondingfive-phase amplifier. In general, coil traces 126 may be grouped suchthat every 5n (n is a positive integer) adjacent coil traces 126 canform one group 134 which may be driven by one corresponding five-phaseamplifier.

FIG. 4A is a schematic partial cross-sectional view of multiple layers128 (128A-128F) of coil traces 126 which may be used in stator 120 ofthe FIG. 1 displacement device 100. It can be seen from FIG. 4A, thatlayers 128A, 128C, 128E comprise Y-oriented coil traces 126Y and thatlayers 128B, 128D, 128F comprise X-oriented coil traces 126X. It canalso be observed from FIG. 4A that Y-oriented coil traces 126Y indifferent layers 128A, 128C, 128E are aligned with one another in theX-direction—i.e. coil traces 126Y in layer 128A are aligned (in theX-direction) with coil traces 126Y in layers 128C, 128E. Although itcan't be directly observed from the illustrated view of FIG. 4A, it canbe appreciated that X-oriented coil traces 126X may exhibit a similarcharacteristic—i.e. coil traces 126X in layer 128B are aligned (in theY-direction) with coil traces 126X in layers 128D, 128F. Coil traces126X, 126Y in the same column (i.e. traces 126X aligned with one anotherin the Y-direction and/or traces 126Y aligned with other another in theX-direction) can be connected in serially, in parallel or independentlyof one another. It will be appreciated that the number of layers 128 canbe any suitable number and is not limited to the six shown in FIG. 4A.

FIG. 4B is a schematic partial cross-sectional view of multiple layers128 (128A, 128C, 128E, 128G) of coil traces 126 which may be used instator 120 of the FIG. 1 displacement device 100. For clarity, onlylayers 128A, 128C, 128E, 128G having Y-oriented traces 126Y are shown inFIG. 4B—i.e. layers 128 having X-oriented coil traces 126X are not shownin FIG. 4B. It can also be observed from FIG. 4B that Y-oriented coiltraces 126Y in different layers 128A, 128C, 128E, 128G are offset fromone another in the X-direction—i.e. coil traces 126Y in layer 128A areoffset from the next adjacent Y-oriented coil traces 126Y in layer 128C,coil traces 126Y in layer 128C are offset from the next adjacentY-oriented coil traces 126Y in layer 128E and so on. In the illustratedembodiment, coil traces 126Y in layers 128A, 128E are aligned with oneanother in the X-direction and coil traces 126Y in layers 128C, 128G arealigned with one another in the X-direction—i.e. coil traces 126Y inevery 2^(nd) layer 128 of Y-oriented coil traces 126Y are aligned withone another in the X-direction.

Although it can't be directly observed from the illustrated view of FIG.4B, it can be appreciated that X-oriented coil traces 126X may exhibitsimilar characteristics—i.e. coil traces 126X in adjacent layers 128B,128D, 128F, 128H of X-oriented coil traces 126X may be offset from oneanother in the Y-direction. In some embodiments, coil traces 126X inevery 2^(nd) layer 128 of X-oriented coil traces 126X are may be alignedwith one another in the Y-direction. Regardless of their offset, thisdescription may refer to coil traces in the same “column”—for example,coil traces 126Y labeled a1, a2, a3, a4 may be referred to as being inthe same column and coil traces 126Y labeled d1, d2, d3, d4 may bereferred to as being in the same column. Coil traces 126X, 126Y in thesame column can be connected in serially, in parallel or independentlyof one another.

The amount of offset between adjacent layers 128 of Y-oriented coiltraces 126Y is referred to as O_(L) and can be used to minimize theeffect of higher order harmonics in the magnetic fields of magnet arrays112. In some embodiments, O_(L) is designed at

${{\pm \frac{\lambda}{10}} + \frac{K\;\lambda}{5}},$where K is a positive integer number. When O_(L) has this characteristicand adjacent Y-oriented traces in a particular column (for example, coiltraces 126Y labeled a1 and a2) are driven with equal current, then theforces between the 5^(th) order harmonic magnetic field generated by amagnet array 112 and two offset traces 126Y in the same column (forexample, coil traces a1 and a2) will tend to cancel one another out(i.e. attenuate one another). In some embodiments, O_(L) is designed at

${{\pm \frac{\lambda}{18}} + \frac{K\;\lambda}{9}},$where K is a positive integer number. When O_(L) has this characteristicand adjacent Y-oriented traces 126Y in a particular column (for example,coil traces 126Y labeled a1 and a2) are driven with equal current, thenthe forces between the 9^(th) harmonic magnetic field generated by amagnet array 112 and two offset traces 126Y in the same column (forexample, coil traces a1 and a2) will cancel one another out (i.e.attenuate one another).

In some embodiments, O_(L) can be designed in such a way that severalharmonic fields are optimally attenuated to minimize overall forceripple effects caused by higher order harmonics of the magnetic fieldgenerated by magnet array 112. In some embodiments, O_(L) is designed at±λ/2 and Y-oriented coils trace of adjacent Y-trace layers (e.g. coiltraces 126Y labeled a1 and a2) are driven with opposite current. As aresult, current flowing into one layer 128 can flow back from anadjacent layer 128 to form winding turns.

Driving Y-oriented traces 126Y in a particular column (for example coiltraces a1 and a2) with equal currents is practical, because these coiltraces 126Y may be serially connected, but may not be desirable toachieve ideal cancellation of 5^(th) order harmonics effects because thecoil trace a1 is closer to the magnet array than the coil trace a2. Insome embodiments, the effects of higher order magnetic field harmonicsof magnet arrays 112 can be further reduced by providing O_(L) asdiscussed above and by driving Y-oriented traces 126Y in a particularcolumn but in different layers 128 (for example, coil traces 126Ylabeled a1 and a2) with different amounts of current. Assuming that coiltrace layer 128A is closer to moveable stage 110 than coil trace 128Cand so on, it will be appreciated that the magnetic field experienced bycoil traces 126Y labeled a1 and a2 will not be identical. Accordingly,further attenuation of the effect of 5^(th) order harmonics of themagnetic field of magnet array 112 may be achieved by setting thecurrent in the traces 126Y of layer 128C to be at least approximatelye^(2π×5×G) ^(L) ^(/λ) times higher than the corresponding current in thetraces 126Y of corresponding columns of layer 128A, where G_(L) is thecenter-to-center Z-direction spacing between Y-oriented coil traces 126Yin adjacent layers 128. For example, the current in coil trace 126Ylabeled a2 can be set to be at least approximately a factor ofe^(2π×5×G) ^(L) ^(/λ) times higher than the corresponding current intrace 126Y labeled a1. The current in the traces 126Y of a single columnof every 2^(nd) layer 128 of Y-oriented coil traces 126Y (e.g. thecurrent in traces 126Y labeled a1 and a3) may be set to be the same.

Similarly, some attenuation of the effect of 9^(th) order harmonics ofthe magnetic field of magnet array 112 may be achieved by setting thecurrent in the traces 126Y of layer 128C to be at least approximatelye^(2π×9×G) ^(L) ^(/λ) times higher than the corresponding current in thetraces 126Y of corresponding columns of layer 128A, where G_(L) is thecenter-to-center Z-direction spacing between Y-oriented coil traces 126Yin adjacent layers 128. For example, the current in coil trace 126Ylabeled a2 can be set to be at least approximately e^(2π×9×G) ^(L) ^(/λ)times higher than the corresponding current in trace 126Y labeled a1.The current in the traces 126Y of a single column of every 2^(nd) layer128 of Y-oriented coil traces 126Y (e.g. the current in traces 126Ylabeled a1 and a3) may be set to be the same.

It will be appreciated that similar offsets and/or similar currentdriving characteristics can be used for X-oriented coils 126X to reducethe effects of higher order magnetic fields associated with magnetarrays 112.

FIG. 5 is a schematic partial view of a single layer 128 of coil traces126 showing a group connection scheme which may be used in displacementdevice 100 of FIG. 1. Layer 128 shown in FIG. 5 comprises a plurality ofY-oriented coil traces 126Y which are grouped into groups 134. Asdiscussed above, coil traces 126Y in a group 134 may be driven by acommon multi-phase amplifier. In the FIG. 5 embodiment, there areN_(G)=8 different groups 134 of coil traces 126Y (labeled Group 1-Group8 in FIG. 5). Each group 134 of coil traces 126Y extends in theY-direction and the groups 134 are laid out side-by-side along the Xdirection in a repeating pattern. In general, the number N_(G) of groups134 of coil traces 126Y may be any suitable positive integer. To reducethe number of amplifiers (not shown) used to implement displacementdevice 100, coil traces 126Y belonging to particular groups 134 may bein serial connection. For example, all of the groups 134 of coil traces126Y labeled Group 1 in FIG. 5 may be serially connected. When two ormore coil traces 126Y in one layer are serially connected, the directionof current flow in such coil traces 126Y may be the same or opposite toone another. Within each group 134, each phase can either be driven byan independent amplifier, such as a H-bridge, or all phases areconnected in a star pattern and driven by a multi-phase amplifier. In aspecial case, each of the FIG. 5 groups 134 includes only a single coiltrace 126Y. At the cost of operational complexity and additionalhardware, this special case embodiment permits maximum flexibility withrespect to control of current location and, in turn, control of themovement of moveable stage 110. In this special case, groups 134 withthe same group label (e.g. Group 1) can be serially connected and thedirection of current flow in these traces 126Y can be the same oropposite to one another. It will be appreciated that similar groupconnection schemes may be used for X-oriented coils 126X in other layers128.

It will be appreciated that even with the group connectionimplementation of FIG. 5, Y-oriented coil traces 126 in the same columnbut in different layers 128 (e.g. coil traces 126Y labeled a1, a2, a3,a4 in FIG. 4B) can also be connected serially and share a commonamplifier. Similarly, it will be appreciated that even with the groupconnection implementation of FIG. 5, X-oriented coil traces 126 in thesame column but in different layers can also be connected serially andshare a common amplifier.

Since each phase of coil traces 126 has capacitance and there ismutual-capacitance among difference phases of coil traces 126, one ormore external inductor(s) (not shown) can be serially inserted betweenan amplifier output terminal and a terminal of coil trace(s) 126. Suchserial inductors can be installed on the planar coil PCB boards, and/oron amplifier circuit boards, and/or in the ends of the cables connectingamplifiers to planar coil assemblies. Adding such serial inductors mayincrease the inductance of the coil load and may thereby reduce thepower loss of switching electronics of power amplifiers and reduce thecurrent ripples in coil traces 126.

Magnet Array

FIGS. 6A and 6B (collectively, FIG. 6) are schematic partialcross-sectional views of layouts of magnet arrays 112 which may be usedin moveable stage 110 of the FIG. 1 displacement device 100 and whichare useful for showing a number of magnet array parameters. It can beobserved that the layout of magnet arrays 112A, 112B, 112C, 112D in FIG.6A is the same as that of magnet arrays 112A, 112B, 112C, 112D in FIG.1B. The layout of magnet arrays 112A, 112B, 112C, 112D in FIG. 6B issimilar to that of magnet arrays 112A, 112B, 112C, 112D shown in FIGS.6A and 1B. The discussion in this section applies to both of the layoutsshown in FIGS. 6A and 6B.

FIG. 6 shows that each magnet array 112 has a width of W_(m) and alength of L_(m). The spacing between two magnet arrays with the sameelongation direction (i.e. between X-magnet arrays 112A, 112C or betweenY-magnet arrays 112B, 112D) is denoted as spacing S_(m). It can beobserved that in the illustrated embodiment, moveable stage 110comprises a non-magnetic region 113 located in a center of its magnetarrays 112 and that the dimensions of non-magnetic region 113 areS_(m)−W_(m) by S_(m)−W_(m). As discussed above, for each magnet array112, the magnetization segments 114 and corresponding magnetizationdirections are uniform along the dimension L_(m) and are orientedorthogonally to the dimension L_(m). For each magnet array 112, themagnetization segments 114 and corresponding magnetization directionvary along the direction of dimension W_(m). While not expressly shownin the illustrated views, the magnet arrays 112 shown in FIG. 6 may bemounted under a suitable table or the like which may be used to supportan article (e.g. a semiconductor wafer) thereatop.

One implementation of magnet arrays 112 is described above in connectionwith FIG. 1D (for Y-magnet array 112B) and 1E (for X-magnet array 112A).In the description of magnet arrays that follows, a comprehensiveexplanation is provided in the context of an exemplary Y-magnet array112B. X-magnet arrays may comprise similar characteristics where the Xand Y directions and dimensions are appropriately interchanged. Forbrevity, in the description of Y-magnet array 112B that follows, thealphabetic notation is dropped and Y-magnet array 112B is referred to asmagnet array 112. Similarly, the magnetization segments 114B of Y-magnetarray 112B are referred to as magnetization segments 114.

FIG. 7A shows an embodiment of a magnet array 112 substantially similarto magnet array 112B described above in connection with FIG. 1D. Magnetarray 112 is divided, along the X-axis, into a number of magnetizationsegments 114 which are generally linearly elongated in the Y-axisdirection. In the illustrated embodiment, the magnetization directionsof magnetization segments 114 have a spatial periodicity with a period(or wavelength) λ along the X-axis; the width W_(m) of magnet array 112in the X-direction is given by W_(m)=N_(m)λ where N_(m) is a positiveinteger (and N_(m)=2 in the FIG. 7A embodiment); the magnetizationdirections of the various magnetization segments 114 are oriented indirections orthogonal to the Y-axis; the X-axis widths of the variousmagnetization segments 114 are either: λ(2N_(t)) for the two outermost(edge) segments 114 or λ/N_(t) for the interior segments 114, whereN_(t) represents the number of different magnetization directions inmagnet array 112 (and N_(t)=4 in the FIG. 7A embodiment); and themagnetization of magnetization segments 114 is mirror symmetric aboutcentral Y-Z plane 118. It will be appreciated that with W_(m)=N_(m)λ andthe magnetization of magnetization segments 114 being mirror symmetricabout central Y-Z plane 118, the outermost (edge) segments 114 haveX-axis widths that are half the X-axis widths of interior segments 114and that the outermost edge segments 114 have magnetizations that areoriented in along the Z-direction.

FIG. 7B is another embodiment of a magnet array 112 suitable for usewith the FIG. 1 displacement device. The FIG. 7B magnet array 112 hascharacteristics similar to those of the FIG. 7A magnet array 112, exceptthat N_(m)=1 and N_(t)=4. It can be observed from FIG. 7B that thespatial magnetic period λ is defined even where the total X-axis widthW_(m) of the magnet array is less than or equal to λ. In the FIG. 7Bcase, the magnetization directions of magnetization segments 114 ofmagnet array 112 may be considered to be spatially periodic in theX-direction with a period λ, even though there is only a single period.

As discussed above, magnet arrays 112 that exhibit the properties ofthose shown in FIGS. 7A and 7B eliminate or reduce cross-coupling forcesfrom coil traces 126 oriented in X directions. Such characteristics ofmagnet arrays 112 shown in FIGS. 7A and 7B include: magnet arrays 112including magnetization segments 114 which are generally elongated inthe Y-direction with corresponding magnetizations oriented orthogonallyto the Y-direction; the X-dimension width W_(m) of magnet arrays 112 isW_(m)=N_(m)λ where N_(m) is an integer and λ is the magnetic period λdescribed above; and magnet arrays 112 are mirror symmetric about a Y-Zaxis that runs though the center of the X-dimension of magnet arrays112.

FIGS. 7C and 7D show other embodiments of magnet arrays 112 suitable foruse with the FIG. 1 displacement device. In these embodiments, themagnetization directions of magnetization segments 114 have a spatialperiodicity with a period (or wavelength) λ along the X-axis; the widthW_(m) of magnet array 112 in the X-direction is given byW_(m)=(N_(m)+0.5)λ where N_(m) is a non-negative integer (and N_(m)=0 inthe FIG. 7C embodiment and N_(m)=1 in the FIG. 7D embodiment); themagnetization directions of the various magnetization segments 114 areoriented in directions orthogonal to the Y-axis; the magnetization ofmagnetization segments 114 is mirror anti-symmetric about central Y-Zplane 118; and the outermost (edge) segments 114 have magnetizationsthat are oriented in the Z-direction and X-axis widths of λ/(2N_(t))=λ/8(where N_(t)=4 in the embodiments of both FIGS. 7C and 7D) which arehalf of the X-axis widths λ/N_(t)=λ/4 for the interior segments 114. Inthe FIG. 7C case, the magnetization directions of magnetization segments114 of magnet array 112 may be considered to be spatially periodic inthe X-direction with a period λ, even though magnet array 112 exhibitsless than a single period λ.

When the width W_(m) of magnet array 112 is a non-integer number ofmagnetic wavelengths λ (as in the case in the embodiments of FIGS. 7Cand 7D, for example), then there will be coupling of force or moment tomagnet array 112 from current flow in non-aligned coil traces 126 thatinteract with the magnetic field of array 112. For example, in the caseof the Y-magnet arrays 112 shown in FIGS. 7C and 7D (which are mirroranti-symmetric about Y-Z plane 118), there will be coupling of moment inthe rotational direction about Z to Y-magnet arrays 112 from currentflow in coil traces oriented along the X-direction. This net moment canbe compensated using suitable control techniques or using suitablearrangements of additional magnetic arrays 112 with different (e.g.opposite) magnetization patterns.

FIGS. 7E-7H show other embodiments of magnet arrays 112 suitable for usewith the FIG. 1 displacement device. In these embodiments, themagnetization directions of magnetization segments 114 have a spatialperiodicity with a period (or wavelength) λ along the X-axis; the widthW_(m) of magnet array 112 in the X-direction is given by W_(m)=N_(m)λ/2,where N_(m) is a positive integer (and N_(m)=1 in the FIG. 7Eembodiment, N_(m)=2 in the FIG. 7F embodiment, N_(m)=3 in the FIG. 7Gembodiment and N_(m)=4 in the FIG. 7H embodiment); the magnetizationdirections of the various magnetization segments 114 are oriented indirections orthogonal to the Y-axis; and the outermost (edge) segments114 have magnetizations that are oriented along the X-axis and X-axiswidths of λ/(2N_(t))=λ/8 (where N_(t)=4 in the embodiments of FIGS. 7Eand 7H) which are half of the X-axis widths λ/N_(t)=λ/4 for the interiorsegments 114. Note that the central Y-Z plane 118 is not explicitlyshown in FIGS. 7E-7H. However, it will be appreciated that this Y-Zplane 118 divides the X-dimension of magnet array 112 in half.

In FIGS. 7E and 7G, the magnetization of magnetization segments 114 ismirror symmetric about central Y-Z plane 118, and the width W_(m) ofmagnet array 112 in the X-direction is not an integer number of spatialperiods λ. In the case of Y-magnet arrays 112 shown in FIGS. 7E and 7G,there will be coupling of forces in the Y direction to Y-magnet arrays112 from current flow in coil traces 126 oriented along the X-direction.This net force can be compensated for using suitable control techniquesor using suitable arrangements of additional magnetic arrays 112 withdifferent (e.g. opposite) magnetization patterns.

In FIGS. 7F and 7H, the magnetization of magnetization segments 114 ismirror anti-symmetric about central Y-Z plane 118, and the width W_(m)of magnet array 112 in the X-direction is an integer number of spatialperiods λ. In the case of Y-magnet arrays 112 shown in FIGS. 7F and 7H,there will be coupling of moment in the rotational direction around Z toY-magnet arrays 112 from current flow in coil traces 126 oriented alongthe X-direction. This net moment can be compensated using suitablecontrol techniques or using suitable arrangements of additional magneticarrays 112 with different (e.g. opposite) magnetization patterns.

FIGS. 7I-7L show other embodiments of magnet arrays 112 suitable for usewith the FIG. 1 displacement device. In these embodiments, themagnetization directions of magnetization segments 114 have a spatialperiodicity with a period (or wavelength) λ along the X-axis; the widthW_(m) of magnet array 112 in the X-direction is given by W_(m)=N_(m)λ/2,where N_(m) is a positive integer (and N_(m)=1 in the FIG. 7Iembodiment, N_(m)=2 in the FIG. 7J embodiment, N_(m)=3 in the FIG. 7Kembodiment and N_(m)=4 in the FIG. 7L embodiment); the magnetizationdirections of the various magnetization segments 114 are oriented indirections orthogonal to the Y-axis; and the X-axis widths of all of themagnetization segments 114 are λ/N_(t) (where N_(t)=4 in the illustratedembodiments of FIGS. 7I-7L. As the magnetization of magnetizationsegments in FIG. 7I-7L is not mirror symmetric about central Y-Z plane118, there will be coupling of moment in the rotational direction aroundZ to Y-magnet arrays 112 from current flow in coil traces oriented alongthe X-direction. In addition, for the cases in FIGS. 7I and 7K, as thewidth W_(m) of magnet array 112 in the X-direction is not an integernumber of spatial periods λ, there will be coupling of forces in the Ydirection to Y-magnet arrays 112 from current flow in coil traces 126oriented along the X-direction. This net force and moment can becompensated using suitable control techniques or using suitablearrangements of additional magnetic arrays 112 with different (e.g.opposite) magnetization patterns.

In some embodiments, magnet arrays 112 of FIGS. 7A-7L may be fabricatedfrom unit magnetization segments 114 having Y-dimension lengths L_(m)and X-dimension widths λ/(2N_(t)) or λ/(N_(t)) where Nt is the number ofmagnetization directions in a period λ as discussed above. In someembodiments, magnetization segments 114 having X-dimension widthsλ/(N_(t)) may be fabricated from a pair of side-by-side magnetizationsegments 114 having X-dimensions widths λ/(2N_(t)) and having theirmagnetization directions oriented in the same direction. In someembodiments, the Z-dimension heights of the unit magnetization segments114 may be same as their X-dimension widths—e.g. λ/(2N_(t)) orλ/(N_(t)).

As discussed above, a central non-magnetic spacer may be provided inmagnet arrays 112. In embodiments which are symmetric or mirrorsymmetric about central Y-Z plane 118, such a non-magnetic spacer maydivide the central magnetization segment 114 into a pair of “half-width”magnetization segments 114 (i.e. having X-dimensions widths similar tothe X-dimension widths of the edge segments 114). The resultant magnetarrays 118 remain symmetric or mirror symmetric about a central Y-Zplane 118. In embodiments which are not symmetric about a central Y-Zplane 118, different patterns may be used.

FIGS. 8A-8L show magnet arrays 112 suitable for use with the FIG. 1displacement device 100 in accordance with particular embodiments. Themagnet arrays 112 of FIGS. 8A-8L have features similar to those ofmagnet arrays 112 of FIGS. 7A-7L, except that the magnet arrays 112 ofFIGS. 8A-8L include non-magnetic spacers 136 centrally located (in theirX-dimensions). Spacers 136 (of the Y-magnet arrays 112 shown in FIGS.8A-8L) may be provided with a X-axis width g which is at leastapproximately equal to

${g = {\left( {\frac{N_{g}}{5} + \frac{1}{10}} \right)\lambda}},$where N_(g) is a non-negative integer number. When the width g ofspacers 136 exhibits this property, spacers 136 will have an attenuating(cancelling) effect on disturbance torques and/or forces created by the5^(th) order harmonic field of magnet array 112. In general, the width gof the non-magnetic spacer 136 may be set to be at least approximatelyequal to

${= {\left( {\frac{N_{g}}{k} + \frac{1}{2k}} \right)\lambda}},$where N_(g) has the above described properties and k is the order of theharmonic of the magnetic field to be attenuated. In some embodiments,spacers 136 (of the Y-magnet arrays 112 shown in FIGS. 8A-8L) may beprovided with a X-axis width g which is at least approximately equal to

${g = {{\frac{K_{g}}{5}\lambda} - W_{c}}},$where K_(g) is a non-negative integer number and W_(c) is the X-axiswidth of coil traces 126 generally elongated in Y direction. When thewidth g of spacers 136 exhibits this property, spacers 136 will have anattenuating (cancelling) effect on disturbance torques and/or forcescreated by the 5^(th) order harmonic field of magnet array 112. Ingeneral, the width g of the non-magnetic spacer 136 may be set to be atleast approximately equal to

${{\frac{K_{g}}{k}\lambda} - W_{c}},$where K_(g) and W_(c) have the above described properties and k is theorder of the harmonic of the magnetic field to be attenuated.

The magnet array 112 embodiments shown in FIGS. 8A and 8B have two sidesarranged on either X-direction side of non-magnetic spacer 136. Both theleft and right sides (in the illustrated view) of the FIG. 8A magnetarray 112 have magnetization patterns similar to those of magnet array112 of FIG. 7A; and both the left and right sides of the FIG. 8B magnetarray 112 have magnetization patterns similar to those of magnet array112 of FIG. 7B. The X-direction width W_(side) of each side of themagnet arrays 112 of FIGS. 8A and 8B (i.e. the X-direction distancebetween an edge of array 112 and the edge of non-magnetic spacer 136) isW_(side)=N_(m)λ where N_(m) is a positive integer and the totalX-direction width of the magnet arrays 112 of FIGS. 8A and 8B isW_(m)=2N_(m)λ+g, where N_(m)=2 in FIG. 8A and N_(m)=1 in FIG. 8B.

The magnet array 112 embodiments shown in FIGS. 8C and 8D have two sidesarranged on either X-direction side of non-magnetic spacer 136. The left(in the illustrated view) sides of magnet arrays 112 shown in FIGS. 8Cand 8D have magnetization patterns similar to those of magnet arrays 112shown in FIGS. 7C and 7D respectively. The right (in the illustratedview) sides of magnet arrays 112 shown in FIGS. 8C and 8DF havemagnetization patterns that are opposite those of the left sides—i.e. asif the left side of the magnet array 112 was duplicated in the locationof the right side of the magnet array 112 and then each individualmagnetization segment 114 in the right side of the magnet array 112 wasrotated 180° about its own central axis along which it is linearlyelongated. The X-direction width W_(side) of each side of the magnetarrays 112 of FIGS. 8C and 8D is W_(side)=(N_(m)−0.5)λ where N_(m) is apositive integer and the total X-direction width of the magnet arrays112 of FIGS. 8C and 8D is W_(m)=(2N_(m)−1)λ+g, where N_(m)=1 in FIG. 8Cand N_(m)=2 in FIG. 8D.

Similarly, the magnet array 112 shown in FIGS. 8E, 8G, 8I, 8K have twosides arranged on either X-direction side of non-magnetic spacer 136,with their respective left (in the illustrated view) sides havingmagnetization patterns similar to FIGS. 7E, 7G, 7I, 7K magnet array 112and their respective right (in the illustrated view) sides havingmagnetization patterns that are the opposite to those of the left (inthe illustrated view sides, where “opposite” has the same meaning asdiscussed above for the case of FIGS. 8C and 8D. The X-direction widthsW_(side) of each side of the magnet arrays 112 of FIGS. 8E, 8G, 8I, 8Kis W_(side)=(N_(m)−0.5)λ where N_(m) is a positive integer and the totalX-direction width of the magnet arrays 112 of FIGS. 8E, 8G, 8I, 8K isW_(m)=(2N_(m)−1)λ+g, where N_(m)=1 in FIG. 8E, N_(m)=2 in FIG. 8G,N_(m)=1 in FIG. 8I, N_(m)=2 in FIG. 8K.

The magnet arrays 112 shown in FIGS. 8F, 8H, 8J, 8L have two sidesarranged on either X-direction side of non-magnetic spacer 136, withboth their left and right sides having magnetization patterns similar tothose of magnet arrays 112 of FIGS. 7F, 7H, 7J, 7L, respectively. TheX-direction width W_(side) of each side of the magnet arrays 112 ofFIGS. 8F, 8H, 8J, 8L is W_(side)=N_(m)λ where N_(m) is a positiveinteger and the total X-direction width of the magnet arrays 112 ofFIGS. 8F, 8H, 8J, 8L is W_(m)=2N_(m)λ+g, where N_(m)=1 in FIG. 8F,N_(m)=2 in FIG. 8H, N_(m)=1 in FIG. 8J, N_(m)=2 in FIG. 8L. The magnetarrays 112 shown in FIGS. 8A-8L may be fabricated in a manner similar tothat described above for FIGS. 7A-7L.

Layout of Magnet Arrays

As discussed above, FIGS. 6A and 6B show layouts of the magnet arrays112 which may be used in moveable stage 110 of displacement device 100in accordance with particular embodiments. In accordance with particularembodiments, when arranging magnet arrays 112 on moveable stage 110, thespacing S_(m) between two adjacent parallel arrays (e.g. between a pairof X-magnet arrays 112, such as X-magnet array 112A and X-magnet array112C in the case of the FIG. 6 embodiment and/or between a pair ofY-magnet arrays 112, such as Y-magnet arrays 112B and Y-magnet arrays112D, in the case of the FIG. 6 embodiment) may be selected to be atleast approximately

${S_{m} = {\left( {N_{S} + \frac{1}{2}} \right)P_{C}}},$where N_(S) is a non-negative integer number and P_(C) is the coil tracepitch discussed above (see FIG. 2). When a plurality of parallel magnetarrays 112 are designed with this spacing characteristic, this spacingcharacteristic will help to minimize or reduce force and/or torqueripples which may be generated by the discrete nature (i.e. finitedimensions) of coil traces 126.

In some embodiments, when arranging magnet arrays 112 on moveable stage110, the spacing S_(m) between two adjacent parallel arrays (e.g.between a pair of X-magnet arrays 112, such as X-magnet array 112A andX-magnet array 112C in the case of the FIG. 6 embodiment and/or betweena pair of Y-magnet arrays 112, such as Y-magnet arrays 112B and Y-magnetarrays 112D, in the case of the FIG. 6 embodiment) may be selected to beat least approximately S_(m)=(2N_(S)+1)λ/12, where N_(S) is anon-negative integer number. When a plurality of parallel magnet arrays112 are designed with this spacing characteristic, this spacingcharacteristic will help to minimize or reduce 6 cycle-per-λ forceand/or torque ripples which may be generated by the interaction between5^(th) harmonics magnetic field of magnet arrays 112 and current flowingin coil traces 126.

In some embodiments, two adjacent parallel magnet arrays 112 (e.g. apair of X-magnet arrays 112, such as X-magnet array 112A and X-magnetarray 112C in the case of the FIG. 6 embodiment and/or a pair ofY-magnet arrays 112, such as Y-magnet arrays 112B and Y-magnet arrays112D, in the case of the FIG. 6 embodiment) may comprise magnetizationsegments 114 with magnetization orientations that are the same as oneanother. This characteristic is shown, for example, in FIG. 9A whereY-magnet array 112B and Y-magnet array 112D comprise magnetizationsegments 114B, 114D with magnetization orientations that are the same asone another. In some embodiments, two adjacent parallel magnet arrays112 may comprise magnetization segments 114 with magnetizationorientations that are the opposites of one another—i.e. as if eachmagnetization segment 114 is individually rotated 180° about acorresponding central axis along which it is linearly elongated. Thischaracteristic is shown, for example, in FIG. 9B, where magnet array112B and magnet array 112D comprise magnetization segments 114B, 114Dwith magnetization orientations that are opposite to one another.

In some embodiments, the spacing S_(m) is designed to be at leastapproximately

${S_{m} = {N_{S}\frac{\lambda}{2}}},$where N_(S) is a positive integer. Where the spacing of adjacentparallel magnet arrays 112 (e.g. a pair of X-magnet arrays 112, such asX-magnet array 112A and X-magnet array 112C in the case of the FIG. 6embodiment and/or a pair of Y-magnet arrays 112, such as Y-magnet arrays112B and Y-magnet arrays 112D, in the case of the FIG. 6 embodiment) aredesigned to have this feature, then the current distribution in theactive coil traces 126 for each parallel magnet array 112 can besubstantially similar in spatial distribution (i.e. in phase), providedthat the parallel magnet arrays 112 have the same magnetization patternand N_(S) is even or the parallel magnet arrays 112 have oppositemagnetization patterns and N_(S) is odd.

As discussed above, the layout of magnet arrays 112 shown in FIGS. 6Aand 6B provides for a non-magnetic region 113 located between magnetarrays 112. In some embodiments, the dimensions (S_(m)−W_(m)) of thisnon-magnetic region 113 may be designed to have the characteristics that(S_(m)−W_(m))≥λ, such that active coil traces 126 for two parallelmagnet arrays 112 don't interfere with one another.

In some embodiments, the dimension L_(m) of magnet arrays 112 shown inFIGS. 6A and 6B is set at least approximately equal to L_(m)=N_(L)λ,where N_(L) is a positive integer number. Where magnet arrays 112exhibit this characteristic, there will be a further reduction in thecoupling force generated between a magnet array 112 and current flowingin coil traces 126 in directions orthogonal to the elongated dimensionof magnet array 112.

The layout of magnet arrays 112 shown in FIGS. 6A and 6B is not the onlypossible layout for magnet arrays 112 that could be used for moveablestage 110 of the FIG. 1 displacement device 100. More particularly, anumber of other possible layouts of magnet arrays 112 suitable for usein moveable stage 110 of the FIG. 1 displacement device 100 are shown inFIGS. 10A-10D.

FIG. 10A shows a schematic cross-sectional view of layout of magnetarrays 112A, 112B, 112C, 112D which may be used for moveable stage 110of the FIG. 1 displacement device 100 in accordance with a particularembodiment. The FIG. 10A layout of magnet arrays 112 differs from theFIG. 6 layout of magnet arrays 112 because magnet arrays 112 are shaped(e.g. as squares) such that non-magnetic region 113 is eliminated andall of the undersurface area of moveable stage 110 is occupied by magnetarrays 112. In the illustrated embodiment of FIG. 10A, each magnet array112 comprises a pattern of magnetization segments 114 having thecharacteristics as those shown in FIG. 7A, although it will beappreciated that magnet arrays 112 of the FIG. 10A layout could beprovided with magnetization segments 114 exhibiting characteristics ofany of the magnet arrays 112 described herein—e.g. exhibiting any of themagnetization patterns shown in FIGS. 7A-7L and 8A-8L.

FIG. 10B shows a schematic cross-sectional view of a layout of magnetarrays 112A-112P which may be used for moveable stage 110 of the FIG. 1displacement device 100 in accordance with another embodiment. Thelayout of FIG. 10B differs from the layout of FIG. 10A in that thelayout of FIG. 10B includes more than four magnet arrays 112. In theillustrated embodiment, magnet arrays 112A, 112C, 112E, 112G, 112I,112K, 112M, 112O are X-magnet arrays and magnet arrays 112B, 112D, 112F,112H, 112J, 112L, 112N, 112P are Y-magnet arrays. The FIG. 10B layoutcomprising more than four magnet arrays 112 may be used, for example,where moveable stage 110 is relatively large.

FIG. 10C shows a schematic cross-sectional view of a layout of magnetarrays 112 which may be used for moveable stage 110 of the FIG. 1displacement device 100 according to another embodiment. For brevity,only Y-magnet arrays 112A1, 112A2, 112A3, 112B1, 112B2, 112B3, 112C1,112C2, 112C3, 112D1, 112D2, 112D3 are expressly labeled in FIG. 10C,although it will be appreciated that X-magnet arrays are also shown inFIG. 10C. Magnet arrays 112 with the same orientation (e.g. X-magnetarrays or Y-magnet arrays) and aligned with one another in the directionorthogonal to the direction of elongation of their magnetizationsegments may be referred to herein as a set of aligned magnet arrays.For example, Y-magnet arrays 112A1, 112A2, 112A3 are a set of alignedY-magnet arrays, because they have the same orientation (they areY-magnet arrays elongated along the Y-axis) and are aligned with oneanother in a direction (the X-direction) orthogonal to the direction ofelongation of their respective magnetization segments. A set of alignedmagnet arrays may be driven by current flow in the same coil traces 126of stator 120 (not shown in FIG. 10C). For example, the set of alignedY-magnet arrays 112A1, 112A2, 112A3 may be driven by current flow in thesame coil traces 126 of stator 120. Similarly, the set of alignedY-magnet arrays 112B1, 112B2, 112B3 may be driven by the same coiltraces 126 of stator 120, the set of aligned Y-magnet arrays 112C1,112C2, 112C3 may be driven by the same coil traces 126 of stator 120 andthe set of aligned Y-magnet arrays 112D1, 112D2, 112D3 may be driven bythe same coil traces 126 of stator 120.

Because of the spacing between each set of aligned Y-magnet arrays (e.g.the set of aligned Y-magnet arrays 112A1, 112A2, 112A3) and the adjacentset(s) of aligned Y-magnet arrays (e.g. the adjacent set of alignedY-magnet arrays 112B1, 112B2, 112B3), each set of aligned Y-magnetarrays can be driven independently by its corresponding active coiltraces 126 without significant coupling from adjacent sets of alignedY-magnet arrays. In the FIG. 10C embodiment, there is also an offsetbetween the actuating force center of the set of aligned Y-magnet arrays112A1, 112A2, 112BA3 and the set of aligned Y-magnet arrays 112B1,112B2, 112B3, these two sets of aligned Y-magnet arrays can be used togenerate two levitating forces (i.e. the Z-direction) and two lateral(i.e. in the X-direction) forces.

In the illustrated embodiment of FIG. 10C, there are four sets ofaligned Y-magnet arrays: a first set of aligned Y-magnet arrays 112A1,112A2, 112A3; a second set of aligned Y-magnet arrays 112B1, 112B2,112B3; a third set of aligned Y-magnet arrays 112C1, 112C2, 112C3; and afourth set of aligned Y-magnet arrays 112D1, 112D2, 112D3, and each setof aligned Y-magnet arrays can independently generate two forces (onelevitation force (in the Z-direction) and one lateral force (in theX-direction)). Three or more sets of aligned Y-magnet arrays having aY-direction offset (e.g. the offset of the actuating force centerbetween the first set of aligned Y-magnet arrays 112A1, 112A2, 112A3 andthe second set of aligned Y-magnet arrays 112B1, 112B2, 112B3) may alonebe used to provide actuating forces and torques in 5 degrees offreedom—i.e. forces in the X and Z directions and moment around the X, Yand Z axes. The only actuating force that cannot be provided by three ormore sets of aligned Y-magnet arrays having a Y-direction offset isforce in the Y-direction in FIG. 10C.

In the illustrated embodiment of FIG. 10C, there are four sets ofaligned Y-magnet arrays: a first set of aligned Y-magnet arrays 112A1,112A2, 112A3; a second set of aligned Y-magnet arrays 112B1, 112B2,112B3; a third set of aligned Y-magnet arrays 112C1, 112C2, 112C3; and afourth set of aligned Y-magnet arrays 112D1, 112D2, 112D3. While notexplicitly enumerated with reference numerals, those skilled in the artwill appreciate that the illustrated embodiment of FIG. 10C also includefour sets of aligned X-magnet arrays, each of which can independentlygenerate two forces (one levitation force (in the Z-direction) and onelateral force (in the Y-direction)). With all of the sets of alignedarrays capable of being independently driven by their correspondingactive coil traces 126, the FIG. 10C magnet array layout provides asignificant amount of over actuation. These over-actuating capabilitiescan be used to control the flexible mode vibration of moveable stage110, for moveable stage shape correction and/or for vibrationsuppression. It will be appreciated by those skilled in the art that thelayout of FIG. 10C provides four sets of aligned X-magnet arrays andfour sets of aligned Y-magnet arrays, but some embodiments may compriselarger numbers or smaller numbers of sets of aligned X and Y-magnetarrays. Also, it will be appreciated by those skilled in the art thatthe layout of FIG. 10C provides that each set of aligned X-magnet arraysand each set of aligned Y-magnet arrays comprises three individualmagnet arrays, but some embodiments may comprise different numbers ofindividual magnet arrays in each set of aligned magnet arrays.

FIG. 10D shows a schematic cross-sectional view of a layout of magnetarrays 112 which may be used for moveable stage 110 of the FIG. 1displacement device 100 according to another embodiment. FIG. 10D alsoschematically depicts the coil traces 126 that may be used to actuatethe various sets of aligned X and Y-magnet arrays 112. It should benoted that the coil traces 126 shown in FIG. 10D are schematic in natureand do not represent the dimensions or numbers of coil traces 126. Thelayout of magnet arrays 112 in FIG. 10D is similar to that of FIG. 10C,except that in FIG. 10D each set of aligned X and Y-magnet arrays 112comprises a pair of individual magnet arrays 112 (instead of threeindividual magnet arrays, as is the case in FIG. 10C). Moreparticularly, the layout of FIG. 10D comprise four sets of alignedX-magnet arrays with two individual magnet arrays in each set and foursets of aligned Y-magnet arrays with two individual magnet arrays ineach set. The sets of X-magnet arrays in the FIG. 10D layout include: afirst set of aligned arrays 112 a 1, 112 a 2; a second set of alignedarrays 112 b 1, 112 b 2; a third set of aligned arrays 112 c 1, 112 c 2;and a fourth set of aligned arrays 112 d 1, 112 d 2. The sets ofY-magnet arrays in the FIG. 10D layout include: a first set of alignedarrays 112A1, 112A2; a second set of aligned arrays 112B1, 112B2; athird set of aligned arrays 112C1, 112C2; and a fourth set of alignedarrays 112D1, 112D2.

As is the case for the layout of FIG. 10C, sets of aligned magnet arraysin the FIG. 10D layout may be driven by the same set of coil traces 126on stator 120. More particularly: the first set of aligned X-magnetarrays 112 a 1, 112 a 2 may be driven by coil traces 126 a 1/a2; thesecond set of aligned X-magnet arrays 112 b 1, 112 b 2 may be driven bycoil traces 126 b 1/b2; the third set of aligned X-magnet arrays 112 c1, 112 c 2 may be driven by coil traces 126 c 1/c2; and the fourth setof aligned X-magnet arrays 112 d 1, 112 d 2 may be driven by coil traces126 d 1/d2. Similarly: the first set of aligned Y-magnet arrays 112A1,112A2 may be driven by coil traces 126A1/A2; the second set of alignedY-magnet arrays 112B1, 112B2 may be driven by coil traces 126B1/B2; thethird set of aligned Y-magnet arrays 112C1, 112C2 may be driven by coiltraces 126C1/C2; and the fourth set of aligned Y-magnet arrays 112D1,112D2 may be driven by coil traces 126D1/D2. It will be appreciated thatthe active coil traces for each set of aligned magnet arrays are notstatic but are determined dynamically based on the current position ofmoveable stage 110 and the desired movement of moveable stage 110.

As is the case with FIG. 10C discussed above, the layout of FIG. 10Dincludes a significant amount of over actuation. These over-actuatingcapabilities can be used to control the flexible modes of moveable stage110, for moveable stage shape correction and/or for moveable stagevibration suppression. It will be appreciated by those skilled in theart that the layout of FIG. 10D provides four sets of aligned X-magnetarrays and four sets of aligned Y-magnet arrays, but some embodimentsmay comprise larger numbers or smaller numbers of sets of aligned X andY-magnet arrays. Also, it will be appreciated by those skilled in theart that the layout of FIG. 10D provides that each set of alignedX-magnet arrays and each set of aligned Y-magnet arrays comprises a pairof individual magnet arrays, but some embodiments may comprise differentnumbers of individual magnet arrays in each set of aligned magnetarrays.

The characteristics of each individual magnet array 112 in the layoutsof FIGS. 10A-10D (e.g. the orientations of magnetization segments 114,the lengths L_(m), the widths W_(m) and the like) can be similar to anyof those described herein—e.g. exhibiting any of the magnetizationpatterns shown in FIGS. 7A-7L and 8A-8L. The spacing S_(m) of adjacentarrays in FIGS. 10C, 10D can be similar to that described above forFIGS. 6A, 6B.

Field Folding and Current Commutation

In some embodiments, magnet arrays 112 comprise characteristics similarto so-called “Halbach arrays”. Usually, the magnetic field of a Halbacharray is assumed to be primarily sinusoidal with a small amount of5^(th) order harmonic distortion. This assumption is relatively accurateat locations well inside (i.e. away from the edges) of a long,multi-period Halbach array. However, at the edges of the Halbach array,the magnetic field is far from sinusoidal, particularly when the magnetarray is only 1-2 magnetic periods (λ) wide as is the case, for example,in some of the magnet arrays 112 shown in FIGS. 7 and 8. The distortionof the magnetic field at the edges of magnet arrays 112 may be referredto as fringing field effects. Designing a commutation law to achieve atleast approximately linear force characteristics for such anon-sinusoidal field can be difficult.

One technique to minimize the fringing field effects when using currentcarrying coil traces to impart forces on a Halbach array involvesincreasing the number of magnetic periods (λ) in the Halbach array.Although disturbance forces attributable to the fringing field areunchanged with the increased number of magnetic periods, the effect ofsuch disturbance forces on the total amount of force imparted on thelarger Halbach array is reduced. Another technique to minimize thefringing field effects when using current carrying coil traces to impartforces on a Halbach array involves only exciting coil traces that arelocated away from the edges of the Halbach array and the fringingfields. This second technique sacrifices force generation capacity.

The inventors have determined that it can be theoretically proven (usingspatial convolution theory) that the forces (both lateral and vertical)between a magnet array of width W_(m) and an infinitely wide currentarray of period W_(m) are of identical magnitudes to the forces betweenan infinitely wide magnet array with period W_(m) and a single coiltrace. This principle is illustrated in FIGS. 11A-11C. FIG. 11A shows ashort Y-magnet array 112 of width W_(m) moving laterally (i.e. in theX-direction in the illustrated view) relative to a single coil trace 126excited with constant current. This FIG. 11A arrangement producesnon-sinusoidal forces due to the interaction of coil trace 126 with thefringing fields at or near the edge of magnet array 112. In FIG. 11B,extra coil traces 126′ excited with the same amount of current asoriginal coil trace 126 are added to form an infinitely wide currentarray of period W_(m). The resulting total force between magnet array112 and the array of coil traces 126, 126′ becomes sinusoidal with asmall component caused by the 5^(th) order harmonic. In FIG. 11C, forcesare generated between the current in a single coil trace 126 and aninfinitely wide periodic magnet array 112 of period W_(m).

The total forces between magnet array 112 and the arrays of coil traces126, 126′ in the arrangement of FIG. 11B are the same as the forcesbetween magnet array 112 and single coil trace 126 in the arrangement ofFIG. 11C, if all coil traces 126, 126′ are excited with the same amountof current. This same principal applies to any of the magnet arrays 112shown in FIGS. 7 and 8. In practical terms, the FIG. 11B infinite coilarray is not required and it is sufficient to excite extra coil tracesup to about λ/2 or greater beyond the edges of magnet array 112. Thisequivalence significantly simplifies the force analysis. Using thisprinciple and standard three phase sinusoidal commutation, the actuatingforce on magnet array 112 (and a moveable stage 110 comprising aplurality of magnet arrays 112) has excellent linear characteristics,which is desirable for high speed precision applications.

FIG. 11D is a schematic cross-sectional view showing one layer 128 ofcoil traces 126 and a single magnet array 112 that may be used in theFIG. 1 displacement device 100 and how the field folding principle ofFIGS. 11A-11C may be used in practice. Active (current carrying) coiltraces 126 are shown as solid black; traces 126 shown in white representeither inactive coil traces 126 or active coil traces 126 for othermagnet arrays (not shown). In the illustrate view of FIG. 11D, magnetarray 112 is a Y-magnet array having magnetization segments 114 whichare generally linearly elongated in the Y-direction. As can be seen fromFIG. 11D, coil traces 126 are excited below magnet array 112 and out toa field folding length L_(FF) beyond each X-axis edges of magnet array112. Coil traces 126 beyond this zone (i.e. greater than L_(FF) awayfrom the X-axis edges of magnet array 112) can be either inactive, or beactivated for other magnet arrays or may also be activated for theillustrated magnet array 112. Depending on the gaps between adjacentmagnet arrays (e.g. the gap S_(m)−W_(m) shown in FIG. 6), L_(FF) can beset a suitable distance which balances the desirability of extendingbeyond the X-axis edges of magnet array 112 and avoiding force couplingwith an adjacent magnet array. In some embodiments, L_(FF) can be set atL_(FF)=N_(ff)λ/2, where N_(ff) is a positive integer. In someembodiments, L_(FF) can be set at anything greater than or equal to λ/2.With a field folding length of L_(FF) on either side of the edges ofmagnet array 112, the current direction and magnitude of commutatinglaws can be designed in the same way as done in the situation wheremagnet array 112 is infinitely extended on both sides. This means thatall active coil traces 126 on the same layer 128 for the same magnetarray 112 follow the same commutation law (most commonly sinusoidalcommutation) except that coil traces 126 have electrical phase shiftsrelative to one another.

FIG. 12 is a schematic cross-sectional view showing one layer 128 ofcoil traces 126 and a single Y-magnet array 112 which are useful fordescribing the determination of current commutation. The FIG. 12 magnetarray 112 is a Y-magnet array 112 meaning that its magnetizationsegments 114 are generally linearly elongated in the Y-direction. FIG.12 shows one active coil trace 126 (shown in black), with all other coiltraces 126 (whether active or inactive) shown in white. FIG. 12 includesa coordinate frame X_(m)-Y_(m)-Z_(m), fixed with magnet array 112, wherethe Z_(m) axis origin is at the bottom surface of magnet array 112, theX_(m) axis origin is in the center of magnet array 112. With thesedefinitions, the magnet field in the space below the bottom surface ofmagnet array 112 can be modeled according to:

$\quad\left\{ \begin{matrix}{{B_{z}\left( {x_{m},z_{m}} \right)} = {B_{0}\mspace{11mu}\cos\mspace{11mu}\left( \frac{x_{m}}{\lambda_{c}} \right)e^{z_{m}\text{/}\lambda_{c}}}} \\{{B_{x}\left( {x_{m},z_{m}} \right)} = {{- B_{0}}\mspace{11mu}\sin\mspace{11mu}\left( \frac{x_{m}}{\lambda_{c}} \right)e^{z_{m}\text{/}\lambda_{c}}}}\end{matrix} \right.$where λ_(c)=λ/2π and (x_(m),z_(m)) is an arbitrary point in the spacebelow the bottom surface of magnet array 112. Although magnet array 112is finite in its X-axis width, its magnetic field can be modelled as ifmagnet array 112 is infinitely extended in the X-direction with theperiodic magnetization pattern of magnetization segments 114continuously repeated. Due to the field folding method used, thismodelling assumption does not significantly impact the accuracy of theforce calculations. As shown in FIG. 12, a coil trace 126 is located(i.e. centered) at (x_(m), z_(m)). Regardless of whether the position(x_(m), z_(m)) of this coil trace 126 is right under magnet array 112 orbeyond the X-dimension edges of magnet array 112, we can excite thiscoil trace 126 for this magnet array 112 according to:

${I = {{{- {kF}_{ax}}\mspace{11mu}\cos\mspace{11mu}\left( \frac{x_{m}}{\lambda_{c}} \right)e^{- \frac{z_{m}}{\lambda_{c}}}} - {{kF}_{az}\mspace{11mu}\sin\mspace{11mu}\left( \frac{x_{m}}{\lambda_{c}} \right)e^{- \frac{z_{m}}{\lambda_{c}}}}}},$Where: I is a current in the trace 126 at the position (x_(m),z_(m));F_(ax) and F_(az) represent the desired forces imparted on magnet array112 in X and Z directions, respectively; k is an actuator constantcoefficient; and the current reference direction (positive currentdirection) is consistent with Y_(m) axis (i.e. if current flows into thepage in FIG. 12 then I is positive). When all active current traces 126for magnet array 112 are excited according to the above commutation law(of course, each trace 126 can have different currentamplitude/direction, since each coil trace 126 has distinct spatiallocation), actuating forces imparted on magnet array 112 will be F_(ax)and F_(az). Coil traces 126 in the same lateral location (e.g. in thesame X-axis location in FIG. 12), but different layers 128 can be eitherserially connected (i.e. having the same current) or individuallycontrolled. When they are serially connected, the desired currentamplitude for coil traces 126 in the same lateral location but indifferent layers 128 can be calculated based on the location of the coiltrace 126 on the uppermost layer 128.

As discussed above, some magnet arrays 112 (e.g. the magnet arrays shownin FIGS. 8A-8L) comprise non-magnetic spacers 136. For such magnetarrays 112, determination of coil trace current can be done by assumingthat non-magnetic spacer 136 is not present and by assuming that eachside of the magnet array 112 is moved toward its center (i.e. toward Y-Zplane 118) by half the width g of spacer 136. This process is shownschematically in FIGS. 13A and 13B, where current commutation iscalculated for the actual FIG. 13A magnet array 112 on the basis of theassumption that the FIG. 13A magnet array 112 has the properties of theFIG. 13B magnet array 112. With these assumptions, the inventors havedetermined that the actual resulting forces will not be equal to thecalculated values (F_(ax),F_(az)), but will be scaled by a scalingfactor (e.g. 95%) which may be fixed using suitable control algorithm(s)and/or the like. Such differences can be accommodated using suitablecontrol techniques, such as setting the desired forces to be slightlylarger than would be desired if spacer 136 was not present. As discussedabove, spacer 136 has the benefit that it can reduce the effect of the5^(th) order harmonic of the magnetic field of magnet array 112.

Sensor Systems

To accurately control the position of moveable stage 110 relative tostator 120 in displacement device 100 (e.g. to the precision desired fora typical lithography process and/or the like), it is desirable to knowthe relative positions of moveable stage 110 and stator 120. Asdiscussed above, the forces imparted on moveable stage 110 depend on therelative spacing between coil traces 126 (on stator 120) and magneticarrays 112 (on moveable stage 110). An issue which can give rise todifficulty for determining these relative positions is motion of stator120 which can be generated by ground vibration, by reaction forces onstator 120 and/or the like. FIG. 14A schematically illustrates oneembodiment of a sensing system 200 for separately measuring thepositions of moveable stage 110 and stator 120 relative to a metrologyframe 202. In the illustrated embodiment, stator 120 is supported by astator frame 204 (which may be supported by the ground or by anothervibration isolation system (not shown)) and moveable stage 110 isfloating above stator 120 under the influence of actuating forces causedby the interaction of magnet arrays and current carrying coil traces asdiscussed above. Stator frame 204 can provide mechanical support andthermal cooling for the coil assembly of stator 120.

Metrology frame 202 is supported by one or more vibration isolationmechanisms 206, which may be passive or active vibration isolationmechanisms 206, such as springs, air cylinders, air bearings and/or thelike. Vibration isolation mechanisms 206 isolate metrology frame 202from ground isolation. Metrology frame 202 may also be fabricated fromsuitable materials (e.g. thermally and mechanically stable materials).In the illustrated embodiment, metrology frame 202 provides a stableposition reference for independently measuring the positions of bothmoveable stage 110 and stator 120 relative to the stable metrology frame202. In the FIG. 14A view, Xm1, Zm1, Zm2 represent a number of thecoordinates of the position of moveable stage 110 with respect tometrology frame 202. Although three dimensions of the relative positionare shown in the FIG. 14A view, it should be understood that there mayactually be 6 or more axis measurements associated with the position ofmoveable stage 110 relative to metrology frame 202. Any suitableposition sensing devices may be used to determine these measurements.Non-limiting examples of suitable position sensors include: laserdisplacement interferometers, two-dimensional optical encoders, lasertriangulation sensors, capacitive displacement sensors and/or the like.

Xs1, Zs2, and Zs2 shown in FIG. 14A represent coordinates of theposition of stator frame 204 with respect to metrology frame 202.Although three dimensions of the relative position are shown in the FIG.14A view, it should be understood that there may actually be 6 or moreaxis measurements associated with the position of stator frame 204relative to metrology frame 202. Because the position of stator frame204 relative to metrology frame 202 has only a small amount ofvariation, many low-cost and short-stroke position sensing devices aresufficient for measuring the position of stator frame 204. Non-limitingexamples of suitable positions sensors include: capacitive displacementsensors, eddy current displacement sensors, optical encoders, lasertriangulation sensors and/or the like. It will be appreciated that whilethe position of stator frame 204 may not be exactly known due tomanufacturing errors, thermal loading and/or the like, these factorscause DC or low-frequency uncertainties in measurement of the positionof stator frame 204 relative to metrology frame 202 and may be overcomeby controlling the position of moveable stage 110 using a control schemehaving sufficiently high gain at low frequencies (e.g. an integratingcontrol element by way of non-limiting example to effectively attenuatethese uncertainties. That is, a control scheme can be designed such thatthe position of moveable stage 110 is adjusted at a rate much fasterthan the low frequency uncertainties associated with the measurement ofthe position of stator frame 204. AC or relatively high frequencycomponents of the position of stator frame 204 are more important. It istherefore desirable to measure these high frequency components usingposition sensors of suitably high bandwidth.

FIG. 14B shows another embodiment of a sensor system 220 for measuring aposition of moveable stage 110. In the illustrated embodiment, moveablestage 110 comprises: a plurality of magnet arrays 112, a moving stagestructure 226 and one or more sensor targets 224. Conveniently, one ormore sensor targets 224 may be located in the space 230 (see FIG. 1B)between magnet arrays 112. Stator frame 204 comprises one or more sensorread heads 222. These heads 222 may be installed inside holes in thecoil assembly of stator 120. Sensor heads 222 may interact optically,electrically, electromagnetically and/or the like with sensor targets224 to measure the relative position of moving stage 110 relative tostator frame 204. By way of non-limiting example: sensor targets 224 maycomprise optical two-dimensional grating plates and sensor heads 222 maycomprise optical encoder read heads; sensor targets 224 may compriseconductive plates with two dimensional grid features and sensor heads222 can comprise capacitive displacement measurement probes; sensortargets 224 can comprise reflective surfaces suitable for interferometryand sensor heads 222 may comprise laser interferometry heads; and/or thelike.

Different position sensing techniques can be combined to provide anoverall system. It will be appreciated that sensor heads 222 could belocated on moveable stage 110 and sensor targets 224 could be located onstator frame 204. Also, in the FIG. 14B embodiment, the position ofmoveable stage 110 is measured relative to stator frame 204. In someembodiments, the same types of sensor targets 224 and sensor heads 222could be located on moveable stage 110 and on a metrology frame 202 tomeasure the position of moveable stage 110 relative to metrology frame202 in a system similar to that of FIG. 14A. Still further, it will beappreciated that FIG. 14B only shows the measurement of one or severaldimensions, but other dimensions may be measured using similartechniques.

FIG. 14C shows another embodiment of a sensor system 240 suitable foruse with the FIG. 1 displacement device 100. Moveable stage 110 isprovided with a plurality of identifiable markers 242 (such as lightemitting diodes (LEDs), reflective marker surfaces and/or the like, forexample). A stereo camera 244 can acquire images of these markers 242and, from the image locations of these markers 242, a suitablyprogrammed controller 246 can determine the spatial positions of thesemarkers 242 relative to stereo camera 244. The FIG. 14C embodiment showsthat multiple moveable stages (e.g. moveable stage 110 and secondmoveable stage 110A having markers 242A) can be sensed using the samecamera 244 and controller 246. Accordingly, system 240 can measure therelative position between two moveable stages 120. It will beappreciated by those skilled in the art that suitable markers can alsobe located on stator frame 204 to obtain the positions of the moveablestages referenced to stator frame 204.

It will be appreciated that the above described sensor systems havetheir own advantages and disadvantages, such as cost, measurementrange/volume, resolution, accuracy, incremental or absolute position,sensitivity to line-of-sight block. Two or more of the above describedsensor systems can be combined to achieve desired performancecharacteristics.

Motion Control

FIG. 15 shows a schematic block diagram of a control system 300 suitablefor use in controlling the FIG. 1 displacement device 100. Controlsystem 300 may be implemented by a suitable programmed controller (notexpressly shown). Such a controller (and components thereof) maycomprise hardware, software, firmware or any combination thereof. Forexample, such a controller may be implemented on a programmed computersystem comprising one or more processors, user input apparatus, displaysand/or the like. Such a controller may be implemented as an embeddedsystem with a suitable user interface comprising one or more processors,user input apparatus, displays and/or the like. Processors may comprisemicroprocessors, digital signal processors, graphics processors, fieldprogrammable gate arrays, and/or the like. Components of the controllermay be combined or subdivided, and components of the controller maycomprise sub-components shared with other components of the controller.Components of the controller, may be physically remote from one another.The controller is configured to control one or more amplifiers (notexpressly shown) to drive current in coil traces 126 and to therebycontrollably move moveable stage 110 relative to stator 120.

In the schematic diagram of FIG. 15, V_(r) represents the referencemotion command signals which define the trajectory of moveable stage 110desired by the application process. V_(r) is typically a vector,prescribing the desired trajectory for moveable stage 110 in a mannerwhich comprises multiple degrees of freedom. Such multiple degrees offreedom may include states corresponding to rigid body motion and/orvibration mode motion. As V_(r) is defined by a specific applicationprocess and from the application process point of view, V_(r) is notnecessarily in the form desired for defining the motion of the center ofgravity of moveable stage 110 and/or the vibration mode coordinateformat. For example, V_(r) may specify the motion of a point on a wafersurface in a photolithography application where the wafer is installedon top of moveable stage 110, instead of specifying the motion of thecenter of gravity of moveable stage 110. In such cases, V_(r) may beconverted to a corresponding vector Φ_(r), defined in a modal coordinateframe of reference, via reference position coordinate transform block302.

The vector Φ_(r) may comprise, for example:

$\Phi_{r} = \begin{bmatrix}q_{r\; 1} \\q_{r\; 2} \\q_{r\; 3} \\q_{r\; 4} \\q_{r\; 5} \\q_{r\; 6} \\q_{r\; 7} \\q_{r\; 8}\end{bmatrix}$where q_(r1), . . . q_(r6) represent desired (reference) motion valuesfor 6 states which define rigid body motion (e.g. 3 translational statesand 3 rotational states) and q_(r7), q_(r8) represent reference valuesfor two flexible vibration mode states. It will be appreciated that someembodiments may use different numbers of rigid body states and/orflexible mode states.

In the schematic diagram of FIG. 15, V_(f) represents the outputs ofposition feedback sensors 305 which includes information relating to themeasured position of moveable stage 110. Typically, V_(f) will also beconverted into a motion vector Φ_(f) in the modal coordinate frame via afeedback position coordinate transform block 304. The vector Φ_(f) maycomprise, for example:

$\Phi_{f} = \begin{bmatrix}q_{f\; 1} \\q_{f\; 2} \\q_{f3} \\q_{f\; 4} \\q_{f5} \\q_{f\; 6} \\q_{f7} \\q_{f\; 8}\end{bmatrix}$where q_(f1), . . . , q_(f6) represents feedback values (e.g. feedbackposition values) for the 6 states which define rigid body motion (e.g. 3translational states and 3 rotational states) and q_(f7), q_(f8)represent feedback values for two flexible vibration mode states.

With Φ_(r) as inputs, a feedforward control force/torque vector F_(f)(modal domain force/torque) may be calculated by a feedforward motioncontroller 306. With Φ_(e)=Φ_(r)−Φ_(f) as inputs, a feedback controlforce/torque vector F_(b) (modal domain force/torque) may be calculatedby a feedback motion controller 308. The total modal domain force/torquevector is calculated as F_(ϕ)=F_(f)+F_(b). An actuator force coordinatetransform block 310 may be used to convert the modal domain force/torquevector F_(ϕ) into force commands F_(a) for each magnet array 112. Foreach magnet array, its corresponding active coil current vector I_(a)(including current values for each trace) can be calculated from F_(a)according to an active coil current commutation algorithm performed byblock 312, as discussed above. According to the position Φ_(f) of movingstage 110, a current coordinate transform may be performed by block 314to determine the coil trace reference current I_(sr) for each group ofstator coil traces 126. For each group of coil traces 126, thisreference current I_(sr) will be: zero (inactive); or the active coilcurrent I_(a) for a particular magnet array 112; or the combination ofthe currents for active coils currents for a plurality of magnet arrays112. The stator coil reference current commands I_(sr) may be providedto power amplifiers 316 to drive moveable stage 110, and the actualstator coil currents provided by amplifiers 316 is represented by I_(s).

All 6 (or even more) degrees-of-freedom of moveable stage 110 may bemeasured for optimum motion control of moveable stage 110. However, incertain situations, some of the sensors or part of a sensor may fail orbecome dysfunctional, or for cost-related reasons, there may be fewersensors installed at certain space within the working volume of moveablestage 110. These are examples of circumstances in which not all 6degrees of positional freedom of moveable stage 110 are measured andwhich may be referred to as under-sensing. Some embodiments provide amotion control method for control of moveable stage 110 in under-sensedcircumstances. When the sensor system does not provide measurement inthe Z-direction (i.e. the levitating direction), the Z-component of thedesired force for each magnet array 112 may be set at a constant level,for example, the Z-component of the force on each magnet array 112 maybe set to a fraction of the gravitational force on moveable stage 110.Further, the above-described commutation equation may be changed to:

${I = {{{- {kF}_{ax}}\mspace{11mu}\cos\mspace{11mu}\left( \frac{x_{m}}{\lambda_{c}} \right)e^{- \frac{z_{0}}{\lambda_{c}}}} - {{kF}_{az}\mspace{11mu}\sin\mspace{11mu}\left( \frac{x_{m}}{\lambda_{c}} \right)e^{- \frac{z_{0}}{\lambda_{c}}}}}},$where a nominal constant vertical position z₀ is used for each magnetarray 112 instead of the actual relative height of the magnet array 112above the coil traces 126, where the nominal constant vertical positionz_(o) is the nominal position of the coil traces 126 in the coordinateframe of the moveable stage. For example, in some embodiments, z_(o)=−1mm. Due to the fact that the Z-direction (levitation) force increaseswhen the height of the magnet array 112 above the coil traces 126decreases, a constant value of z₀ will result in a passive levitatingeffect. This passive levitating effect may be relatively moresusceptible to external forces than active control of the Z-direction ofmoveable stage 110, but this passive levitating effect can still ensurethat moveable stage 110 is floating above stator 120 without mechanicalcontact. By way of non-limiting example, this passive Z-directioncontrol strategy is useful when it is desired to move moveable stage 110within a non-critical working zone, for lower cost applications, forapplication which are otherwise more tolerant to positional uncertaintyand/or the like.

A special case under-sensed scenario may occur where sensed positionmeasurement of moveable stage 110 is only available for the X and Ytranslational position and for the rotational degree of freedom aroundZ. In this case, the above-described passive control mechanism canensure stability in the Z translation direction, rotation around the Xaxis and rotation around the Y axis.

Multiple Moveable Stages

In certain applications, such as photo-lithography, automated assemblysystems and/or the like, there can be a desire to simultaneously andindependently control more than one moveable stage. This may beachieved, for example, by providing a corresponding plurality ofindependently controllable stators and controlling the movement of onemoveable stage on each stator. In some circumstances, it is desirable tointerchange the moveable stages (e.g. to move a moveable stage from onestator to another stator).

FIGS. 16A-16D schematically depict a method 400 for interchangingmoveable stages 110 between multiple stators 120 according to oneembodiment of the invention. More particularly, method 400 involves themovement of moveable stage 110A from stator 120A to stator 120B andmoveable stage 110B from stator 120B to stator 120A. Method 400 involvesthe use of at least one intermediate stator 120C. In FIG. 16A, moveablestages 110A and 110B are shown operating on their respective stators120A, 120B. In FIG. 16B, moveable stage 110A is moved from stator 120Ato intermediate stator 120C. In FIG. 16C, moveable stage 110B is movedfrom stator 120B to stator 120A. In FIG. 16D, moveable stage 110A ismoved from intermediate stator 120C to stator 120B.

FIG. 17A schematically depicts a method 420 for interchanging moveablestages 110 between multiple stators 120 according to another embodimentof the invention. Stators 102A, 120B are independently controlled. In aninitial stage of method 420, moveable stage 110A works on stator 120Aand moveable stage 110B works on stator 120B, concurrently andindependently. To swap stators, moveable stage 110A and moveable stage110B can be caused to move in the arrows shown in FIG. 17A. Thismovement imparts momentum on moveable stages 110A, 110B. When the twomoveable stages 110A, 110B (or more precisely their correspondingX-magnet arrays 112) overlap along the X-direction (i.e. when someX-oriented coil traces extend under X-magnet arrays 112 of both moveablestages 110A, 110B), then the “shared” X-oriented coil traces (or all ofthe X-oriented coil traces) can be turned off, while desired Y-orientedcoil traces remain active. Due to the over-actuation discussed above,the system may still actively control the motion of moveable stages110A, 110B with 5 degrees of freedom (with Y-direction translation beingthe only uncontrolled motion). Because of their Y-direction momentum,the two moveable stages 110A, 110B can smoothly pass one another withouttouching or bumping into each other. It should be noted that the meetinglocation of two stages 110A, 110B is not necessarily at the borders oftwo stators 120A, 120B. In general this meeting location can be anywhereon any stator 120A, 120B or between the two stators 120A, 120B.

FIG. 17B schematically depicts how two moveable stages 110A, 110B can becontrolled with six degrees of freedom of motion for each moveable stageon one stator 120. In the FIG. 17B embodiment, the two moveable stages110A, 110B (or, more precisely, their corresponding magnet arrays 112)have non-overlapping locations in the X-direction and partiallyoverlapping locations in the Y-direction. Accordingly, with theillustrated configuration, the X-oriented coil traces for moveablestages 110A, 110B can be independently activated, but moveable stages110A, 110B (or more precisely the magnet arrays 112 of moveable stages110A, 110B) share a number of Y-oriented coil traces. However, with theconfiguration shown in FIG. 17B, there are also a number of Y-orientedcoil traces that only extend under one or more magnet arrays 112 ofmoveable stage 110A and a number of Y-oriented coil traces that onlyextend under one or more magnet arrays 112 of moveable stage 110B. The“shared” Y-oriented coil traces can be de-activated, but with the activeX-oriented coil traces and at least some independently controllableY-oriented coil traces, moveable stages 110A, 110B can still beindependently controlled with 6 degree-of-freedom. In the illustratedconfiguration of FIG. 17B, moveable stages 110A, 110B are shownimmediately adjacent one another in the Y-direction. While thisconfiguration is possible, it is not necessary and moveable stages 110A,110B can be spaced apart in the Y-direction. Further, in FIG. 17B,moveable stages 110A, 110B (or more precisely their magnet arrays 112)are shown at partially overlapping locations in the Y-direction, butmoveable stages 110A, 110B (or more precisely their magnet arrays 112)could also be independently controlled if they were spaced apart fromone another in the X-direction (i.e. completely non-overlapping in theY-direction). The moveable stages in FIG. 17B could be made to pass oneanother in the X-direction and/or the Y-direction using the techniquedescribed above in FIG. 17A—e.g. moveable stage 110A could be moved tothe right (in the illustrated view) of moveable stage 110B or moveablestage 110A could be moved below (in the illustrated view) moveable stage110B. It will be appreciated that an analogous situation could occurwith the two moveable stages 110A, 110B (or more precisely their magnetarrays 112) have non-overlapping locations in the Y-direction andpartially overlapping (or non-overlapping) locations in the X-direction.

In some applications, it may be desirable to move moveable stages 110through a number of different stages. FIG. 18 schematically illustratesan apparatus 460 suitable for this purpose. In the illustratedembodiment, moveable stages 110A-110D move between several stators120A-120F and, in some applications, may stop at each stator 120 forsome operation. In general, there may be any suitable number of moveablestages 110 and any suitable number (greater than the number of moveablestages 110) of stators 120. On each stator 120A-120F, a motion controlsystem of the type described herein may be used to control positions ofthe corresponding moveable stage 110A-110D. In some embodiments,precision position control may only be required inside stators120A-120F. Consequently, stator-to-stator motion may be guided byrelatively inexpensive positions measurement systems, such as indoorGPS, stereo camera and/or the like.

Rotary Displacement Device

There is industrial demand for rotary displacement devices which havesome Z-direction motion (e.g. on the scale of millimeters) together withrotary motion about the Z-axis. FIG. 19A is a horizontal cross-sectionalview of a rotary displacement device 500 according to an embodiment ofthe invention. FIGS. 19B and 19C respectively depict a bottomcross-sectional view of the moveable stage (rotor) 510 of displacementdevice 500 and a top view of the stator 520 of displacement device 500.As can be seen best from FIG. 19B, moveable stage 510 comprises a magnetarray 512 having magnetization segments 514 which are elongated inradial directions and which have circumferentially orientedmagnetization directions. As is the case with the XY moveable stagesdiscussed above, the orientation of the magnetization directions ofmagnetization segments 514 are generally orthogonal to the directions inwhich they are longitudinally extended—i.e. in the case of rotarydisplacement device 500, the circumferential orientation ofmagnetization directions of magnetization segments 514 is generallyorthogonal to the directions (radial) in which magnetization segments514 are physically elongated.

In the illustrated embodiment, magnet array 512 has an angular spatialmagnetization period λ. In some embodiments, the number of spatialmagnetic periods λ in magnet array 512 is a positive integer numberN_(m). In the particular case of the illustrated embodiment, N_(m)=8, sothe angle subtended by each spatial magnetic period is λ=360°/8=45°. Inother embodiments, N_(m) can have a different value. In someembodiments, magnet array 512 may comprise a non-integer number ofspatial magnetic periods λ. By way of non-limiting example, in someembodiments magnet array 512 could comprise (N_(m)+0.5)λ spatialmagnetic periods. As is the case with the XY embodiments describedherein, the width of each magnetization segment 514 is a function of thenumber N_(t) of magnetization directions in a full spatial magneticperiod λ. In the case of the illustrated embodiment, N_(t)=4 and so theangular width of each magnetization segment 514 is λ/N_(t)=λ/4=11.25°.In some embodiments, N_(t) can have a different value.

FIG. 19C shows how stator 520 comprises plurality of radially orientedcoil traces 526. It will be appreciated that current travelling radiallyin coil traces 526 is capable of imparting force on magnet array 112 inboth circumferential directions (e.g. directions having X and/or Ycomponents) and in the Z-direction. In the particular case of theillustrated embodiment, coil traces 526 are divided into a plurality(e.g. four) of groups (labeled Groups 1-4) and shown delineated bydashed lines. Because of the geometrical location of the groups of coiltraces 526, coil traces 526 in Groups 1 and 3 impart Z-direction andprimarily Y-direction forces on magnet array 512, while coil traces inGroups 2 and 4 impart Z-direction and primarily X-direction forces onmagnet array 512. The Z-direction forces can be controlled to generateZ-direction translation as well as rotation about the X and Y axes. TheX and Y-direction forces can be controlled to generate torques (andcorresponding rotation) about the Z-axis and can also be controlled togenerate X and Y translation (if desired). Accordingly, with suitablecontrol of current in coil traces 526, moveable stage 510 ofdisplacement device 500 can be precisely controlled as a rotarydisplacement device, but can also be controlled with all six degrees offreedom. It will be appreciated that the particular grouping of coiltraces 526 shown in FIGS. 19A-C represents only one possible embodiment.As is the case with any of the XY embodiments described herein, eachcoil trace 526 may be individually controlled for maximum flexibility.Also, different grouping arrangements of coil traces 526 may also beprovided. Coil traces 526 may be connected serially or in parallel toachieve various design objectives.

In the illustrated embodiment, stator 520 comprises a plurality (e.g.four) sensor heads 521 which interact with one or more correspondingsensor targets 519 on moveable stage 510 to measure or otherwise senserotary orientation of moveable stage 510 about the Z-axis and X and Ytranslational positions of moveable stage 510. In one particularembodiment, sensor heads 521 comprise encoder read heads and sensortarget 519 comprises an encoder disk. In the illustrated embodiment,stator 520 also comprises a plurality (e.g. four) capacitive sensors 523which can be used to measure or otherwise detect the Z-direction heightof moveable stage 510 relative to stator 520 and the rotationalorientation of moveable stage 510 about the X and Y axes. It will beappreciated that the sensors shown in the particular embodiment of FIG.19 represent only one particular embodiment of a suitable sensor systemwhich may be used with a rotary displacement device, such as rotarydisplacement device 500 and that other sensing systems could be used.

FIG. 19D is a bottom cross-sectional view of a moveable stage (rotor)510′ according to another embodiment which may be used with displacementdevice 500 (i.e. in the place of moveable stage 510. Moveable stage 510′differs from moveable stage 510 in that moveable stage 510′ comprises aplurality of angularly spaced apart magnet arrays 512′. In the case ofthe illustrated embodiment, moveable stage 510′ comprises four magnetarrays 512′. Each magnet array 512′ has an angular spatial magnetizationperiod λ. In some embodiments, the number of spatial magnetic periods λin each magnet array 512′ is a positive integer number N_(m), such thatthe angle subtended by each array is W_(m)=N_(m)λ. In the particularcase of the FIG. 19D embodiment, N_(m)=1. In some embodiments, N_(m) canhave a different value. In some embodiments, the angle subtended by eacharray 512 is W_(m)=(N_(m)+0.5)λ where N_(m) is a non-negative integer.As is the case with the XY embodiments described herein, the width ofeach magnetization segment 514 is a function of the number N_(t) ofmagnetization directions in a full spatial magnetic period λ. In thecase of the illustrated embodiment, N_(t)=4 and so the angular width ofeach magnetization segment 514 is λ/N_(t)=λ/4. In some embodiments,N_(t) can have a different value. In some embodiments, magnet arrays 512can comprise magnetization segments 514 having angular widths ofλ/2N_(t). As in the case of the XY embodiments described above, such“half-width” magnetization segments 514 having angular widths λ/2N_(t)may be provided at the edges of magnet array 512, although this is notnecessary and such half-width magnetization segments can be used atother locations.

FIG. 19E is a top view of a stator 520′ according to another embodimentwhich may be used with displacement device 500 (i.e. in the place ofstator 520). Stator 520′ differs from stator 520 in that stator 520′comprises a plurality of layers 528A, 528B (e.g. two in the case of theillustrated embodiment) of coil traces 526′ wherein the coil traces 526′in adjacent layers 528A, 528B are spatially (angularly) offset from oneanother by an offset angle O_(L). In some embodiments, the offset angleO_(L) can be set at least approximately to

${{\pm \frac{\lambda}{10}} + \frac{K\;\lambda}{5}},$where K is an integer number. When the offset angle O_(L) exhibits thisproperty, this offset can tend to cancel force/torque ripples which maybe caused by the fifth order harmonic magnetic fields of magnet arrays512. It should be noted that both the moveable stage 510′ of FIG. 19Dand the stator 520′ of FIG. 19E can be used at the same time.Other Layouts and Configurations

FIG. 20A schematically depicts a displacement device 600 according toanother embodiment. Displacement device 600 comprises a moveable stage(not explicitly shown) which comprises a plurality of magnet arrays 612.In the illustrated embodiment, displacement device 600 comprise threemagnet arrays 612 (labeled 612A, 612B, 612C). Each magnet array 612A,612B, 612C comprises a corresponding plurality of magnetization segments614A, 614B, 614C which are generally linearly elongated at a particularorientation in the X-Y plane—for example, magnetization segments 614A ofmagnet array 612A have one orientation of linear elongation,magnetization segments 614B of magnet array 612B have a secondorientation of linear elongation and magnetization segments 614C ofmagnet array 612C have a third orientation of linear elongation. As isthe case with the other displacement devices described herein, themagnetization directions of magnetization segments 614A, 614B, 614C maybe generally orthogonal to the direction that they are physicallyelongated. Other than for their relative orientations, thecharacteristics of magnet arrays 612 and magnetization segments 614 maybe similar to those discussed above for magnet arrays 112 andmagnetization segments 114.

Displacement device 600 also comprises a stator (not explicitly shown)that comprises a plurality of generally linearly elongated coil traces626. In the illustrated embodiment, displacement device 600 comprisethree sets of coil traces 626 (labeled 626A, 626B, 626C) which may belocated on corresponding layers (not explicitly shown) of the stator.Each layer of coil traces 626A, 626B, 626C may comprise coil traces626A, 626B, 626C that are generally linearly elongated at a particularorientation in a corresponding X-Y plane. Such layers and theircorresponding coil traces 626A, 626B, 626C may overlap one another (inthe Z-direction) in the working region of displacement device 600. Otherthan for their relative orientations, the characteristics of coil traces626 may be similar to those of coil traces 126 discussed above.

Displacement device 600′ shown in FIG. 20B is similar to displacementdevice 600, except that the orientations of the linearly elongated coiltraces 626A′, 626B′, 626C′ are different than the orientations of thelinearly elongated traces 626A, 626B, 626C and the orientations at whichmagnetization segments 614A′, 614B′ and 614C′ extend are different thanthe orientations at which magnetization segments 614A, 614B, 614Cextend.

FIG. 20C schematically depicts a displacement device 700 according toanother embodiment. Displacement device 700 comprises a moveable stage(not explicitly shown) which comprises a plurality of magnet arrays 712.In the illustrated embodiment, displacement device 700 comprises twomagnet arrays 712 (labeled 712A, 712B). Each magnet array 712A, 712Bcomprises a corresponding plurality of magnetization segments 714A, 714Bwhich are generally linearly elongated at a particular orientation inthe X-Y plane—for example, magnetization segments 714A of magnet array712A have one orientation of linear elongation and magnetizationsegments 714B of magnet array 712B have a second orientation of linearelongation. As is the case with the other displacement devices describedherein, the magnetization directions of magnetization segments 714A,714B may be generally orthogonal to the direction that they arephysically elongated. Other than for their relative orientations, thecharacteristics of magnet arrays 712 and magnetization segments 714 maybe similar to those discussed above for magnet arrays 112 andmagnetization segments 114.

Displacement device 700 also comprises a stator (not explicitly shown)that comprises a plurality of generally linearly elongated coil traces726. In the illustrated embodiment, displacement device 700 comprise twosets of coil traces 726 (labeled 726A, 726B) which may be located oncorresponding layers (not explicitly shown) of the stator. Each layer ofcoil traces 726A, 726B may comprise coil traces 726A, 726B that aregenerally linearly elongated at a particular orientation in acorresponding X-Y plane. Such layers and their corresponding coil traces726A, 726B may overlap one another (in the Z-direction) in the workingregion of displacement device 700. Other than for their relativeorientations, the characteristics of coil traces 726 may be similar tothose of coil traces 126 discussed above.

It will be appreciated that displacement device 700 of the FIG. 20Cembodiment will not be able to provide all six degrees of freedom. Withsuitable control techniques, the embodiment of FIG. 200 C may be capableof providing motion with 4 degrees of freedom.

FIGS. 20A-20C are useful to demonstrate a feature of one aspect andparticular embodiments of the invention. Some of the herein-describedembodiments include relatively large numbers of magnet arrays. Whilethis can achieve over-actuation which may enhance the ability to controlthe movement of the moveable stage relative to the stator, this is notnecessary. Particular embodiments may comprise moveable stages havingany suitable plurality (as few as two) magnet arrays, wherein each suchmagnet array comprises a plurality of magnetization sections that aregenerally linearly elongated along a corresponding direction, providedthat the directions of linear elongation of all of the magnet arraysspan the X-Y plane of the moveable stage. While the preferred directionsof linear elongation may comprise at least two orthogonal directions(which may make control calculations relatively more simple), this isnot necessary. In the case where the magnet arrays are aligned in asingle moveable stage XY plane, any two or more non-parallel directionsof linear elongation will span the XY plane. In currently preferredembodiments where six degrees of freedom are desired, three of moremagnet arrays are provided with at least two of the magnet arrays beinglinearly elongated in non-parallel directions and with the force-centersof the three magnet arrays being non-co-linear. In addition, thedirections of magnetization of the magnetization segments in each magnetarray are generally orthogonal to the direction in which themagnetization segments are linearly elongated. Within a magnet array,the magnetization of the magnetization segments may have characteristicssimilar to any of those described herein—see FIGS. 7 and 8 for example.

Similarly, particular embodiments may comprise stators having coiltraces elongated in any suitable plurality of directions, provided thatthe directions of linear elongation of the coil traces span a notionalX-Y plane of the stator. While the preferred directions of linearelongation may comprise at least two orthogonal directions (which maymake control calculations relatively more simple), this is notnecessary. Any two or more non-parallel directions of linear elongationwill span the notional XY plane of the stator. The XY plane of thestator may be referred to as a notional XY plane, since coil traceshaving different directions of linear elongation may be provided ondifferent layers as discussed above. Such layers may have differentlocations in the Z-direction. Accordingly, the notional XY plane of thestator may be thought of as though the coil traces in each such layerwere notionally brought to a single XY plane having a correspondingsingle location along the Z-axis.

The description set out above describes that there may be differentnumbers N_(t) of magnetization directions within a magnetic spatialperiod λ. However, N_(t)=4 for all of the illustrated embodimentsdescribed above. FIGS. 21A-21C schematically depict magnet arrays 802A,802B, 802C having different values of N_(t)—i.e. different numbers ofmagnetization directions within a particular magnetic period λ. Magnetarray 802A of FIG. 21A has N_(t)=4, magnet array 802B of FIG. 21B hasN_(t)=2 and magnet array 802C of FIG. 21C has magnet array N_(t)=8. Thenumber N_(t) may be selected to be any suitable number, with theadvantage of having relatively large N_(t) is that relatively largeN_(t) provides the corresponding magnet array with a relatively largefundamental harmonic and relatively small higher order harmonics at theexpense of possibly greater cost and complexity in fabricating themagnet array.

As discussed above, the coil layouts shown in FIGS. 3D-3F (whereW_(c)=λ/5) have an advantage that they may result in cancellation orattenuation of some of the effects of the 5^(th) order harmonic of themagnetic field created by a magnet array 112. FIG. 22A schematicallyshows a coil trace layout according to another embodiment which may beused in displacement device 100. Coil traces 126 in the FIG. 22Aembodiment are skewed in the XY plane of moveable stage 110 by an amountO_(c) over the trace length L_(m). In some embodiments, the amount ofskew O_(c) (which may be understood to be the X-direction distancetraversed by Y-oriented trace 126 over its Y-dimension length L_(m)) maybe selected to be λ/5 or λ/9 or λ/13 so as to result in attenuation ofthe 5^(th), or 9^(th) or 13^(th) order harmonic of the magnetic fieldcreated by a magnet array 112. This skew amount O_(c) may be adjusted toattenuate other harmonics by setting O_(c)=λ/n, where n is the number ofthe harmonic for which attenuation is desired. In the FIG. 22Aembodiment, the x-dimension width W_(m) of coil trace 126 is shown asbeing λ/6, but this is not necessary in general and the Y-dimensionwidth W_(m) may have other values. By way of non-limiting example, otherthan for the skew mentioned above, the layout of the FIG. 22A coil tracesimilar to any of the layouts shown in FIGS. 3A-3F).

It will be appreciated that Y-oriented coil traces 126 that are skewedin the manner shown in FIG. 22A will result in some possibly undesirablecoupling between the Y-oriented coils and the X-magnet arrays 112. Thatis, current flowing in Y-oriented coil traces having the skew shown inFIG. 22A may impart forces or torques on X-magnet arrays 112. In thecase of Y-oriented coil traces 126, such cross-coupling may be reducedor minimized by skewing the Y-oriented coil traces 126 in alternatinglayers 128 of Y-oriented traces 126 in opposing directions to have acanceling or attenuating effect on this cross coupling. FIG. 22Bschematically illustrates a pair of adjacent layers 128 of Y-orientedcoil traces 126. For clarity, the X-oriented coils between the layers128 of Y-oriented coils 126 are not expressly shown. The Y-oriented coiltraces 126 in adjacent layers 128 of the FIG. 22B embodiment are skewedin opposite directions in the X-Y plane. This opposing skew of the coiltraces 126 in adjacent layers 128 may be used to reduce or minimizeundesirable coupling between Y-oriented coils 126 and X-magnet arrays112, while simultaneously reducing the effect of the 5th order harmonicof the magnetic field of the magnet arrays 112. As in the variousembodiments of coil traces 126 described above, coil traces 126 indifferent layers 128 may be electrically connected in series, inparallel and/or individually.

FIGS. 23A-23D show various embodiments of Y-oriented coil traces 126which (while generally linearly elongated in the Y-direction) exhibit aspatial triangle-wave which extends in the X-direction over a totalX-direction peak-to-peak amplitude O_(c) and Y-direction spatial periodτ_(C). In the illustrated embodiment, Y-direction spatial period τ_(c)is set to an integer factor of the Y-direction length L_(m) (e.g. L_(m)in FIG. 23A, L_(m)/2 in FIG. 23B, L_(m)/3 in FIG. 23C and L_(m)/4 inFIG. 23D) and the amplitude O_(c) is set to λ/5. These twocharacteristics of Y-oriented coil trace 126 can reduce the effect ofthe cross-coupling of Y-oriented trace with X-magnet arrays 112 and canalso help to attenuate the effects of the 5th order harmonic of themagnetic field of arrays 112 on a single layer 128 of coil traces. Itwill be appreciated that setting the value of O_(c) to have differentvalues can be used to cancel other harmonics (e.g. the 9^(th) orderharmonic or the 13^(th) order harmonic) by setting O_(c)=λ/n, where n isthe number of the harmonic for which attenuation is desired. Y-orientedcoil traces 126 on adjacent Y-oriented layers 128 may be fabricated tohave opposing triangular wave phase (e.g. opposing in the X-direction).FIGS. 23E and 23F show similar spatially periodic square wave andsinusoidal waveforms for Y-oriented coil traces 126, wherein theY-direction spatial period τ_(c) is set to an integer factor of theY-direction length L_(m) and the peak to peak amplitude O_(c) is set toλ/5 to attenuate the effect of the 5th order harmonic of magnet arrays112.

FIG. 24C schematically depicts a Y-oriented coil trace 126 which resultsfrom the superposition of the square wave coil trace 126 of FIG. 24A andthe triangular wave coil trace 126 of FIG. 24B. The FIG. 24A square wavehas a spatial period T_(c1) and an amplitude O_(c1) and the FIG. 24Btriangular wave has a spatial period τ_(c2) and an amplitude O_(c2).Preferably, the spatial periods τ_(c1) and τ_(c2) are both set to aninteger factor of the Y-direction length L_(m) of the coil 126. Theamplitudes O_(c1) and O_(c2) may be set to different levels to attenuatethe effects of more than one harmonic order of the magnetic field ofmagnet arrays 112. In general, the value of O_(c1) and O_(c2) may be setto different levels of O_(c1)=λ/n and O_(c2)=λ/m, where n and m are thenumbers of the harmonics for which attenuation is desired.

In addition to or in the alternative to varying the linear elongation ofcoils 126 in effort to attenuate the effects of higher order harmonicsof the magnetic fields of magnet arrays 112, some embodiments, mayinvolve varying the linear elongation of magnet arrays 112 and theirmagnetization segments 114. FIG. 25A shows a magnet array 112 accordingto another embodiment which may be used in displacement device 100.Magnet array 112 shown in the illustrated embodiment of FIG. 25A is aY-magnet array and its Y-dimension L_(m) is divided into a plurality ofsub-arrays 112A, 112B, 112C, each of which is offset in the X-directionby a distance O_(m) from its adjacent sub-array. In the illustratedembodiment, sub-arrays 112A, 112C at the extremities of magnet array 112have Y-dimensions of L_(m)/4 and sub-array 112B in the middle of magnetarray 112 has a Y-dimension of L_(m)/2. In the illustrated embodiment,sub-arrays 112A, 112C are aligned with one another in the X-directionand are both offset in the X-direction from sub-array 112B by a distanceO_(m). In some embodiments, it may be possible that sub-array 112C isoffset from sub-array 112B in the same X-direction as sub-array 112B isoffset from sub-array 112A.

In some embodiments, the offset O_(m) may be set at least approximatelyequal to

${O_{m} = {\left( {\frac{N_{m}}{5} - \frac{1}{10}} \right)\lambda}},$where N_(m), is any integer number. Setting O_(m) to have thischaracteristic will tend to attenuate or cancel the effects of theinteraction of the 5^(th) order harmonic of the magnet field of magnetarray 112 with coil traces 126 that carry current in the Y-direction,thereby reducing or minimizing associated force ripples. In someembodiments, the offset O_(m) may be set at least approximately equal toO_(m) is set at

${\left( {\frac{N_{m}}{9} - \frac{1}{18}} \right)\lambda},$to attenuate me effects of the interaction of the 9^(th) order harmonicof the magnetic field of magnet array 112 with coil traces 126 thatcarry current in the Y-direction. In some embodiments, the offset O_(m)may be set at least approximately equal to

${O_{m} = {{\frac{N_{m}}{5}\lambda} - W_{c}}},$where N_(m) is any integer number and W_(C) is the X-axis width of coiltraces 126 generally elongated in Y direction. Setting O_(m) to havethis characteristic will tend to attenuate or cancel the effects of theinteraction of the 5^(th) order harmonic of the magnet field of magnetarray 112 with coil traces 126 that carry current in the Y-direction,thereby reducing or minimizing associated force ripples. In someembodiments, the offset O_(m) may be set at least approximately equal toO_(m) is set at

${{\frac{N_{m}}{9}\lambda} - W_{c}},$to attenuate the effects of the interaction of the 9^(th) order harmonicof the magnetic field of magnet array 112 with coil traces 126 thatcarry current in the Y-direction.

In some embodiments, magnet arrays 112 may be provided with differentnumbers of sub-arrays. FIG. 25B shows a particular embodiment where theY-dimension L_(m) of Y-magnet array 112 comprises a pair of sub-arrays112A, 112B, each having a Y-dimension of L_(m)/2 and offset from oneanother by a distance O_(m) in the X-direction. The offset distanceO_(m) of the FIG. 25B sub-arrays 112A, 112B can have the samecharacteristics as the offset distance O_(m) of the FIG. 25A sub-arrays.While magnet array 112 shown in the illustrated embodiment of FIG. 25Acomprises three sub-arrays and magnet array 112 shown in the illustratedembodiment of FIG. 25B comprises two sub-arrays, magnet arrays 112 maygenerally be provided with any suitable number of sub-arrays havingcharacteristics similar to those shown in FIGS. 25A and 25B.

FIGS. 25C and 25D show a number of embodiments of magnet arrays 112which may be used to attenuate the effects of multiple spatial harmonicsof their corresponding magnetic fields. FIGS. 25C and 25D show oneembodiment of a Y-magnet array 112, which comprises six sub-arrayshaving Y-direction lengths

$\frac{L_{m}}{8}$(labeled a,b,c,t,g,h in FIG. 25D) and one sub-array having Y-directionlength

$\frac{L_{m}}{4}$(labeled a-e in FIG. 25D), where L_(m) is the total Y-direction lengthof magnet array 112. FIG. 25D shows how some of sub-arrays (a, b, c,d-e, f, g, h) are shifted or offset (in the X-direction) relative to oneanother. In the embodiment of FIGS. 25C and 25D, sub-arrays b and g arealigned in the X-direction, sub-arrays a and h are shifted (rightwardlyin the illustrated view) relatively to sub-arrays b and g by an amountO_(m2), sub-arrays d and e (together sub-array d-e) are shifted(rightwardly in the illustrated view) relatively to sub-arrays b and gby an amount O_(m1) and sub-arrays c and f are shifted (rightwardly inthe illustrated view) relatively to sub-arrays b and g by an amount2O_(m2)+O_(m1). Each sub-array a,b,c,d-e,f,g,h of the illustratedembodiment has a X-dimension width W_(m). Mirror symmetry on line A-A(at the center of the Y-dimension L_(m) of magnet array 112) reduces orminimizes moment and/or force disturbance on the FIG. 25C, 25D magnetarray 112. The harmonics attenuated by the FIG. 25C, 25D arrangementhave spatial wavelengths equal to 2O_(m1) and 2O_(m2). For example, bysetting O_(m1)=λ/10 and O_(m2)=λ/26, the 5^(th) and 13^(th) harmonics ofthe magnetic field are attenuated. In general, by settingO_(m1)=λ(M−0.5)/p, O_(m1)=λ(N−0.5)/q will greatly minimize disturbancemoment/force resulting from harmonic magnetic fields of wavelength(spatial period) both λ/p and λ/q, where M and N are arbitrary integernumbers.

The techniques illustrated in FIGS. 25C-25D can be extrapolated so thatfield-induced disturbance moment and/or force effects associated withany suitable number of harmonics may be simultaneously attenuated usinga suitable variation of these techniques. It is also possible toattenuate the field-induced effects of one harmonic order, but retainsome level of net moment disturbance (such as shown in FIG. 25B).

Like the skewed coil traces 126 of FIGS. 22A, 22B and the spatiallyperiodic coil traces 126 of FIGS. 23A-23F and 24C, magnet arrays 112 ofparticular embodiments can be skewed or provided with spatialperiodicity along the direction that their respective magnetizationsegments 114 are generally linearly elongated. Such skewing and/orspatial periodicity of magnet arrays 112 may be used to reduce orminimize the effects of higher order harmonics of the magnetic fields ofthese magnet arrays 112. FIG. 26A shows a Y-magnet array 112 which isgenerally linearly elongated in the Y-direction, but which is skewed byan amount O_(p) in the X-direction over its Y-dimension length L_(m).Assuming that the FIG. 26A magnet array 112 is configured to interactwith coil traces 126 having a rectangular geometry with a coil widthW_(c) as defined above, then the skew amount may be set to be at leastapproximately equal to a non-negative value O_(p)=kΛ_(f)−W_(c), whereΛ_(f) is the wavelength of the spatial harmonic of the magnetic fieldthat is to be attenuated and k is a positive integer number. Forexample, if it desired to attenuate the effects of the 5^(th) orderharmonic filed of the FIG. 26A magnet array 112, then O_(p) can be setto be kλ/5−W_(c) where k is a positive integer number.

FIGS. 26B and 26C show spatially periodic Y-magnet arrays 112, whereinan edge of each array 112 varies in the X-direction by an amount O_(p)over it Y-dimension length L_(m). The magnet arrays 112 of FIGS. 26B and26C are periodic with a spatial period τ_(m) where τ_(m)=L_(m) in theFIG. 26B array and τ_(m)=L_(m)/2 in the FIG. 26C array. Like the case ofthe spatially periodic coil traces discussed above, the spatial periodτ_(m) may generally be set to be an integer factor of the Y-dimensionlength L_(m). Also, similar to the case of the spatially periodic coiltraces discussed above, spatially periodic magnet arrays may be providedwith spatially periodic waveforms other than triangular waveforms, suchas square waves, sinusoidal waveforms or superposed waveforms. Thepeak-to-peak amplitude parameter O_(p) can have the characteristics ofthe term O_(p) discussed above in connection with FIG. 26A.

In some embodiments, a combination of skewed coil traces and slantedmagnet arrays may also be usefully implemented to eliminate internalstresses in the magnetic arrays while reducing or minimizing the effectsof the interaction of current carrying coil traces with higher orderharmonics of the magnetic fields of the magnet arrays.

While a number of exemplary aspects and embodiments are discussedherein, those of skill in the art will recognize certain modifications,permutations, additions and sub-combinations thereof. For example:

-   -   The coil traces shown in the embodiment of FIGS. 22, 23 and 24        are Y-oriented coil traces. It will be appreciated that        X-oriented coil traces could be provided with similar        characteristics. Similarly, the magnet arrays shown in the        embodiments of FIGS. 25 and 26 are Y-magnet arrays, but it will        be appreciated that X-magnet arrays could be provided with        similar characteristics. Also, the magnet arrays shown in the        embodiments of FIGS. 25 and 26 have a particular pattern of        magnetization. In general, these magnet arrays may be provided        with any suitable magnetization pattern, such as any of those        shown in FIGS. 7 and 8, for example.    -   For the purpose of minimizing or reducing eddy currents induced        by the motion of magnet arrays 112 on moveable stage 110, coil        traces 126 may be made relatively narrow. In some embodiments,        each coil trace 126 may comprise a plurality of sub-traces 126′.        Such an embodiment is shown schematically in FIG. 27A (in top        view) and in 27B (in cross-section). In coil traces 126A, 126B,        126C of FIG. 27A, each coil trace 126A, 126B, 126C comprises a        plurality of corresponding sub-traces 126A′, 126B′, 126C′        (collectively, sub-traces 126′) where each sub-trace 126′ has a        width T_(c) that is a fraction of the width W_(c) of its        corresponding coil 126. Each sub-trace 126′ only carries a        portion of the current flowing through its corresponding trace        126. Each sub-trace 126′ in the FIG. 27A embodiment is insulated        from its adjacent sub-trace 126′ by an insulator of width T_(f),        although it is not generally necessary for the insulator width        T_(f) to be uniform within a coil trace 126 and there is a        desire to minimize Tf, to achieve high surface fill factor. In        general, any suitable number of sub-traces 126′ may be provided        in each trace 126 depending on the trace width W_(c), the        sub-trace width T_(c) and the insulation with T_(f). The        sub-traces 126′ of each corresponding coil trace 126 may be        electrically connected in parallel at their ends (e.g. at their        Y-dimension ends in the case of the illustrated embodiment). The        regions where sub-traces 126′ are connected to one another may        be outside of the working region of device 100—i.e. outside of        the range of motion of moveable stage 110, although this is not        necessary. In other embodiments, sub-traces 126′ may be serially        connected with one another. Coil sub-traces 126′ may be        fabricated using known PCB fabrication technology. FIG. 27B        shows a cross-sectional view of one particular trace 126 and its        corresponding sub-traces 126′.    -   Coil traces 126 may be fabricated using techniques other than        PCB technology. Any conductor that is or may be shaped to be        generally linearly elongated may be used to provide coil traces        126. FIGS. 28A and 28B show one example with coils 122 in an        active region 124 of stator 120 comprising coil traces 126        having round cross-sections. FIG. 28B shows detail of how traces        126 are generally linearly elongated in the X and Y directions        to provide alternating layers 128 of traces X-oriented traces        126X and Y-oriented traces 126Y. Each trace 126 shown in FIGS.        28A and 28B may be made up of further sub-traces of various        cross-sections. FIG. 28C shows one example, wherein a trace 126        having circular cross-section comprises a plurality of        sub-traces 126′ having circular cross-section. One common method        for implementing this trace would be to use standard        multi-filament wire with an external insulator. FIG. 28D shows        one example of a coil trace 126 having rectangular cross-section        with sub-traces 126′ of circular cross-section.    -   In the illustrated embodiments, coil traces 126 on different        layers 128 are shown as being the same as one another. In some        embodiments, coil traces 126 on different layers 128 and/or coil        traces 126 with different orientations (e.g. X-orientations and        Y-orientations) may have properties that are different from one        another. By way of non-limiting example, X-oriented coil traces        126 may have a first coil width W_(c1) and/or coil pitch P_(c1)        and Y-oriented coil traces 126 may have a second coil width        W_(c2) and/or coil pitch P_(c2) which may be the same or        different from those of the X-oriented coil traces 126. Other        properties of coil traces 126 could additionally or        alternatively be different from one another. Similarly, magnet        arrays 112 (e.g. magnet arrays 112 of different orientations        (e.g. X-magnet arrays and Y-magnet arrays 112) or even magnet        arrays 112 with the same orientations) are shown as being the        same as one another. In some embodiments, different magnet        arrays 112 may have properties that are different from one        another. By way of non-limiting example, X-magnet arrays could        have first widths W_(m1) and/or spatial periods λ₁ and Y-magnet        arrays may have second widths W_(m2) and/or spatial periods λ₂.        Other properties of magnet arrays 112 could additionally or        alternatively be different from one another.    -   In this description and the accompanying claims, elements (such        as layers 128, coil traces 126, moving stages 110 or magnet        arrays 112) are said to overlap one another in or along a        direction. For example, coil traces 126 from different layers        128 may overlap one another in or along the Z-direction. When it        is described that two or more objects overlap in or along the        Z-direction, this usage should be understood to mean that a        Z-direction-oriented line could be drawn to intersect the two or        more objects.    -   In the description and drawings provided herein, moveable stages        are shown as being static with their X, Y and Z axes being the        same as the X, Y and Z axes of the corresponding stator. This        custom is adopted in this disclosure for the sake of brevity. It        will of course be appreciated from this disclosure that a        moveable stage can (and is designed to) move with respect to its        stator, in which case the X, Y and Z axes of the moveable stage        may no longer be the same as (or aligned with) the X, Y and Z        axes of its stator. Accordingly, in the claims that follow, the        X, Y and Z axes of the stator are referred to as the stator        X-axis, the stator Y-axis and the stator Z-axis and the X, Y and        Z axes of the moveable stage are referred to as the stage        X-axis, the stage Y-axis and the stage Z-axis. Corresponding        directions may be referred to as the stator X-direction        (parallel to the stator X-axis), the stator Y-direction        (parallel to the stator Y-axis), the stator Z-direction        (parallel to the stator Z-axis), the stage X-direction (parallel        to the stage X-axis), the stage Y-direction (parallel to the        stage Y-axis) and the stage Z-direction (parallel to the stage        Z-axis). Directions, locations and planes defined in relation to        the stator axes may generally be referred to as stator        directions, stator locations and stator planes and directions,        locations and planes defined in relation to the stage axes may        be referred to as stage directions, stage locations and stage        planes.    -   In the description above, stators comprise current carrying coil        traces and moveable stages comprise magnet arrays. It is of        course possible that this could be reversed—i.e. stators could        comprise magnet arrays and moveable stages could comprise        current carrying coil traces. Also, whether a component (e.g. a        stator or a moveable stage) is actually moving or whether the        component is actually stationary will depend on the reference        frame from which the component is observed. For example, a        stator can move relative to a reference frame of a moveable        stage, or both the stator and the moveable stage can move        relative to an external reference frame. Accordingly, in the        claims that follow, the terms stator and moveable stage and        references thereto (including references to stator and/or stage        X, Y, Z-directions, stator and/or stage X,Y,Z-axes and/or the        like) should not be interpreted literally unless the context        specifically requires literal interpretation Moreover, unless        the context specifically requires, it should be understood that        the moveable stage (and its directions, axes and/or the like)        can move relative to the stator (and its directions, axes and/or        the like) or that the stator (and its directions, axes and/or        the like) can move relative to a moveable stage (and its        directions, axes and/or the like).

While a number of exemplary aspects and embodiments have been discussedabove, those of skill in the art will recognize certain modifications,permutations, additions and sub-combinations thereof. It is thereforeintended that the following appended claims and claims hereafterintroduced are interpreted to include all such modifications,permutations, additions and sub-combinations as are within their truespirit and scope.

What is claimed is:
 1. A method for effecting displacement between firstand second moveable stages on a stator, the method comprising: providinga stator comprising a plurality of elongated coils shaped to provide aworking region wherein traces of the coils are generally linearlyoriented, the plurality of elongated coils comprising: a first pluralityof coil traces distributed over a first layer at a corresponding firststator Z-location, the first plurality of coil traces generally linearlyelongated in a stator X-direction in the first layer; and a secondplurality of coil traces distributed over a second layer at acorresponding second stator Z-location, the second plurality of coiltraces generally linearly elongated in a stator Y-direction in thesecond layer, the stator Y-direction generally orthogonal to the statorX-direction; the first and second layers overlapping one another in astator Z-direction in the working region, the stator Z-directiongenerally orthogonal to both the stator X-direction and the statorY-direction; and providing a first moveable stage comprising: a firstfirst magnet array comprising a plurality of first first magnetizationsegments generally linearly elongated in a stage X-direction, each firstfirst magnetization segment having a magnetization direction generallyorthogonal to the stage X-direction and at least two of the first firstmagnetization segments having magnetization directions that aredifferent from one another; and a first second magnet array comprising aplurality of first second magnetization segments generally linearlyelongated in a stage Y-direction generally orthogonal to the stageX-direction, each first second magnetization segment having amagnetization direction generally orthogonal to the stage Y-directionand at least two of the first second magnetization segments havingmagnetization directions that are different from one another; providinga second moveable stage comprising: a second first magnet arraycomprising a plurality of second first magnetization segments generallylinearly elongated in the stage X-direction, each second firstmagnetization segment having a magnetization direction generallyorthogonal to the stage X-direction and at least two of the second firstmagnetization segments having magnetization directions that aredifferent from one another; and a second second magnet array comprisinga plurality of second second magnetization segments generally linearlyelongated in the stage Y-direction generally orthogonal to the stageX-direction, each second second magnetization segment having amagnetization direction generally orthogonal to the stage Y-directionand at least two of the second second magnetization segments havingmagnetization directions that are different from one another; causingthe first moveable stage to move past the second moveable stage in thestator X-direction, wherein causing the first moveable stage to movepast the second moveable stage in the stator X-direction comprises:imparting momentum on the first moveable stage in the stator-X directionby selectively driving current in at least one driver coil trace of thesecond plurality of coil traces to thereby effect movement of the firstmoveable stage in the stator X-direction relative to the second moveablestage; overlapping a first portion of the first moveable stage with afirst portion of the second moveable stage in the stator Y-direction;after imparting momentum on the first moveable stage in the stator-Xdirection, using the momentum of the first moveable stage to cause thefirst moveable stage to move in the stator X-direction at least until asecond portion of the first moveable stage is non-overlapping with asecond portion of the second movable stage in the stator Y-direction byselectively reducing current in at least one shared coil trace of thesecond plurality of coil traces, the at least one shared coil tracecomprising a coil trace that overlaps at least one first secondmagnetization segment and at least one second second magnetizationsegment in the stator Z-direction; after the second portion of the firstmoveable stage is non-overlapping with the second portion of the secondmovable stage in the stator Y-direction, controlling the first moveablestage in the stator X-direction by selectively driving current in atleast one non-shared coil trace of the second plurality of coil traces,the at least one non-shared coil trace overlapping only one or morefirst second magnetization segments of the first moveable stage fromamong the first second and second second magnetization segments.
 2. Themethod according to claim 1 wherein selectively reducing current in theat least one shared coil trace of the second plurality of coil tracescomprises turning off the at least one shared coil trace of the secondplurality of coil traces.
 3. The method according to claim 1 wherein theat least one driver coil trace of the second plurality of coil traces ison a first stator X-direction side of each second second magnetizationsegment.
 4. The method according to claim 1 wherein the at least onenon-shared coil trace is on a second stator X-direction side, opposite afirst stator X-direction side, of each second second magnetizationsegment.
 5. The method according to claim 1 comprising controlling thefirst moveable stage in the stator Y-direction while causing the firstmoveable stage to move past the second moveable stage in the statorX-direction.
 6. The method according to claim 5 wherein controlling thefirst moveable stage in the stator Y-direction comprises selectivelydriving current in the first plurality of coil traces to cause relativemovement between the second moveable stage and the stator.
 7. The methodaccording to claim 1 wherein selectively reducing current in the atleast one shared coil trace of the second plurality of coil tracescomprises reducing current in each of the shared coil traces of thesecond plurality of coil traces.
 8. The method according to claim 1wherein overlapping the at least a first portion of the first moveablestage with the first portion of the second moveable stage in the statorY-direction comprises driving current in at least one coil trace of thesecond plurality of coil traces to thereby effect movement of the firstmoveable stage in the stator X-direction relative to the second moveablestage until the at least a first portion of the first moveable stageoverlaps with the first portion of the second moveable stage in thestator Y-direction.
 9. The method according to claim 1 whereinoverlapping the at least a first portion of the first moveable stagewith the first portion of the second moveable stage in the statorY-direction comprises using the momentum of the first moveable stage tocause the first moveable stage to move in the stator X-direction untilthe at least a first portion of the first moveable stage overlaps withthe first portion of the second moveable stage in the statorY-direction.
 10. The method according to claim 1 wherein selectivelyreducing the current in the at least one shared coil trace of the secondplurality of coil traces comprises selectively reducing the current inthe at least one shared coil trace of the second plurality of coiltraces when more than half of a stage X-direction dimension of the firstmoveable stage overlaps the second moveable stage in the statorY-direction.
 11. The method according to claim 1 wherein the at least afirst portion of the first moveable stage comprises at least one firstsecond magnetization segment.
 12. The method according to claim 1wherein the at least a second portion of the first moveable stagecomprises at least one first second magnetization segment.
 13. Themethod according to claim 1 wherein the magnetization directions of theplurality of first magnetization segments exhibit a first spatialmagnetic period λ₁ over a stage Y-direction width W_(m1) of the firstmagnet array and the magnetization directions of the plurality of secondmagnetization segments exhibit a second spatial magnetic period λ₂ overa stage X-direction width W_(m2) of the second magnet array.
 14. Themethod according to claim 1 wherein the first moveable stage comprises:a first third magnet array comprising a plurality of first thirdmagnetization segments generally linearly elongated in the stageX-direction, each first third magnetization segment having amagnetization direction generally orthogonal to the stage X-directionand at least two of the first third magnetization segments havingmagnetization directions that are different from one another; and afirst fourth magnet array comprising a plurality of first fourthmagnetization segments generally linearly elongated in the stageY-direction, each first fourth magnetization segment having amagnetization direction generally orthogonal to the stage Y-directionand at least two of the first fourth magnetization segments havingmagnetization directions that are different from one another.
 15. Themethod according to claim 14 wherein the second moveable stagecomprises: a second third magnet array comprising a plurality of secondthird magnetization segments generally linearly elongated in the stageX-direction, each second third magnetization segment having amagnetization direction generally orthogonal to the stage X-directionand at least two of the second third magnetization segments havingmagnetization directions that are different from one another; and asecond fourth magnet array comprising a plurality of second fourthmagnetization segments generally linearly elongated in the stageY-direction, each second fourth magnetization segment having amagnetization direction generally orthogonal to the stage Y-directionand at least two of the second fourth magnetization segments havingmagnetization directions that are different from one another.
 16. Themethod according to claim 14 wherein the stage locations of the firstfirst and first third magnet arrays are offset from one another in thestage X-direction.
 17. The method according to claim 16 wherein thestage locations of the first first and first third magnet arrays areoffset from one another in the stage X-direction by a first offsetdistance, the first offset distance less than a stage X-direction lengthL_(m1) of the first first magnet array.
 18. The method according toclaim 16 wherein the first first and first third magnet arrays arespaced apart from one another in the stage Y-direction.
 19. The methodaccording to claim 18 wherein the first second and first fourth magnetarrays are offset from one another in the stage Y-direction.
 20. Themethod according to claim 19 wherein the first second and first fourthmagnet arrays are spaced apart from one another in the stageX-direction.